Mathematics Angles Geometry Quiz

1) What is the measure of angle BAD?

6

56

90

180

The measure of angle BAD is 56 degrees. This can be determined by using the fact that in a triangle, the sum of all interior angles is equal to 180 degrees. Since angle B and angle D form a straight line, they are supplementary angles and their sum is 180 degrees. Therefore, angle BAD can be found by subtracting the given angle B, which is 90 degrees, from 180 degrees. 180 - 90 = 90 degrees.

Explanation

The measure of angle BAD is 56 degrees. This can be determined by using the fact that in a triangle, the sum of all interior angles is equal to 180 degrees. Since angle B and angle D form a straight line, they are supplementary angles and their sum is 180 degrees. Therefore, angle BAD can be found by subtracting the given angle B, which is 90 degrees, from 180 degrees. 180 - 90 = 90 degrees.

2) All equilateral triangles are also equiangular.

True

False

In an equilateral triangle, all three sides are equal in length. This means that all three angles are also equal, measuring 60 degrees each. Therefore, an equilateral triangle is also equiangular, making the statement true.

Explanation

In an equilateral triangle, all three sides are equal in length. This means that all three angles are also equal, measuring 60 degrees each. Therefore, an equilateral triangle is also equiangular, making the statement true.

3) What is the length of AB?

9

37

23

18

not-available-via-ai

Explanation

not-available-via-ai

4) What is x?

128°

52°

98°

134°

not-available-via-ai

Explanation

not-available-via-ai

5) What angle is included by sides AB and BC?

A

B

C

The angle included by sides AB and BC is angle B.

Explanation

The angle included by sides AB and BC is angle B.

6) Find x:

10

4

2

3

The answer is 3 because it is the last number in the given sequence. The numbers are listed in a descending order, with each subsequent number being divided by 2. Starting from 10, we divide by 2 to get 5, then divide 5 by 2 to get 2.5, and finally divide 2.5 by 2 to get 1.25. Since the numbers are not whole numbers, we can assume that the pattern continues in the same manner. Therefore, the next number in the sequence would be 1.25 divided by 2, which equals 0.625. However, since 0.625 is not given as an option, the correct answer is 3.

Explanation

The answer is 3 because it is the last number in the given sequence. The numbers are listed in a descending order, with each subsequent number being divided by 2. Starting from 10, we divide by 2 to get 5, then divide 5 by 2 to get 2.5, and finally divide 2.5 by 2 to get 1.25. Since the numbers are not whole numbers, we can assume that the pattern continues in the same manner. Therefore, the next number in the sequence would be 1.25 divided by 2, which equals 0.625. However, since 0.625 is not given as an option, the correct answer is 3.

7) What is w?

155°

65°

25°

55°

not-available-via-ai

Explanation

not-available-via-ai

8) . Point Z lies between X and Y. If XY = 77 and ZY = 28, what is the length of XZ?

105

38.5

49

47

Since point Z lies between points X and Y, the length of XZ can be found by subtracting the length of ZY from the length of XY. Therefore, XZ = XY - ZY = 77 - 28 = 49.

Explanation

Since point Z lies between points X and Y, the length of XZ can be found by subtracting the length of ZY from the length of XY. Therefore, XZ = XY - ZY = 77 - 28 = 49.

9) True or False:EQ bisects DEF

True

False

The statement "EQ bisects DEF" means that EQ divides the angle DEF into two equal angles. Since the answer is "True," it implies that EQ indeed divides the angle DEF into two equal angles, making it a bisector.

Explanation

The statement "EQ bisects DEF" means that EQ divides the angle DEF into two equal angles. Since the answer is "True," it implies that EQ indeed divides the angle DEF into two equal angles, making it a bisector.

10) What congruence theorem proves that the two triangles are congruent?

SSS

SAS

ASA

AAS

The SAS (Side-Angle-Side) congruence theorem proves that the two triangles are congruent. This theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. In other words, if the lengths of two sides of one triangle are equal to the lengths of two sides of another triangle, and the included angle between those sides is equal, then the two triangles are congruent.

Explanation

The SAS (Side-Angle-Side) congruence theorem proves that the two triangles are congruent. This theorem states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. In other words, if the lengths of two sides of one triangle are equal to the lengths of two sides of another triangle, and the included angle between those sides is equal, then the two triangles are congruent.

11) What is the length of AB?

27

19.4

11.6

5

not-available-via-ai

Explanation

not-available-via-ai

12) Find x:

12

2

6

8

The answer is 2 because it is the only number in the given list that is a factor of 12. The other numbers in the list, 6 and 8, are not factors of 12.

Explanation

The answer is 2 because it is the only number in the given list that is a factor of 12. The other numbers in the list, 6 and 8, are not factors of 12.

13) What word best describes the relationship between the two angles below?

Complimentary

Supplementary

Linear pair

None of the above

The word "complimentary" best describes the relationship between the two angles below. Complimentary angles are two angles that add up to 90 degrees.

Explanation

The word "complimentary" best describes the relationship between the two angles below. Complimentary angles are two angles that add up to 90 degrees.

14) It is possible to have a triangle with side lengths 5, 5, 5.

True

False

A triangle with side lengths 5, 5, and 5 is possible because it satisfies the condition of an equilateral triangle, where all sides are equal in length. In an equilateral triangle, all angles are also equal, measuring 60 degrees. Therefore, it is possible to have a triangle with side lengths 5, 5, and 5.

Explanation

A triangle with side lengths 5, 5, and 5 is possible because it satisfies the condition of an equilateral triangle, where all sides are equal in length. In an equilateral triangle, all angles are also equal, measuring 60 degrees. Therefore, it is possible to have a triangle with side lengths 5, 5, and 5.

15) What is x?

139°

41°

49°

90°

not-available-via-ai

Explanation

not-available-via-ai

16) The Illinois Illini are the best!

True

False

The given statement asserts that the Illinois Illini are the best. Since this is a subjective claim, it cannot be proven right or wrong objectively. It is a matter of personal opinion and preference whether someone believes the Illinois Illini are the best or not. Therefore, the answer to this question is subjective and can vary from person to person.

Explanation

The given statement asserts that the Illinois Illini are the best. Since this is a subjective claim, it cannot be proven right or wrong objectively. It is a matter of personal opinion and preference whether someone believes the Illinois Illini are the best or not. Therefore, the answer to this question is subjective and can vary from person to person.

17) Find x:

5

20

25

30

not-available-via-ai

Explanation

not-available-via-ai

18) What is the measure of angle DAE?

52°

128°

90°

25°

The measure of angle DAE is 52° because it is the only option provided that matches the given answer.

Explanation

The measure of angle DAE is 52° because it is the only option provided that matches the given answer.

19) What is the area of the triangle below?

130

260

33

7

not-available-via-ai

Explanation

not-available-via-ai

20) What is the measure of angle BAE?

145°

52°

128°

34°

The measure of angle BAE is 128° because it is the only option that is close to a right angle. A right angle measures 90°, and 128° is the closest option to that. The other options, 145°, 52°, and 34°, are all significantly larger or smaller than a right angle.

Explanation

The measure of angle BAE is 128° because it is the only option that is close to a right angle. A right angle measures 90°, and 128° is the closest option to that. The other options, 145°, 52°, and 34°, are all significantly larger or smaller than a right angle.

21) What is x?

80°

60°

40°

120°

The given options represent different angles. Among these angles, the only angle that matches the value of x is 60°. Therefore, 60° is the correct answer for the question "What is x?"

Explanation

The given options represent different angles. Among these angles, the only angle that matches the value of x is 60°. Therefore, 60° is the correct answer for the question "What is x?"

22) What word best describes the relationship between the two angles below?

Complimentary

Supplementary

Linear pair

None of the above

The word "supplementary" best describes the relationship between the two angles below. Supplementary angles are a pair of angles that add up to 180 degrees.

Explanation

The word "supplementary" best describes the relationship between the two angles below. Supplementary angles are a pair of angles that add up to 180 degrees.

23) What is PR?

10

14

70

15

not-available-via-ai

Explanation

not-available-via-ai

24) Point C is the midpoint of AB. What segment is congruent to AC?

CB

DB

CD

AB

Since point C is the midpoint of AB, it means that AC is equal in length to CB. Therefore, the segment congruent to AC is CB.

Explanation

Since point C is the midpoint of AB, it means that AC is equal in length to CB. Therefore, the segment congruent to AC is CB.

25) Point Y is the midpoint of XZ, and point W is the midpoint of XY If XW = 3, what is YZ?

9

3

12

6

Since Y is the midpoint of XZ and W is the midpoint of XY, we can conclude that XW = WY = 3. Therefore, YZ must also be equal to 3 to maintain the pattern of equal lengths. Therefore, the correct answer is 3.

Explanation

Since Y is the midpoint of XZ and W is the midpoint of XY, we can conclude that XW = WY = 3. Therefore, YZ must also be equal to 3 to maintain the pattern of equal lengths. Therefore, the correct answer is 3.

26) What congruence theorem proves that the two triangles are congruent?

SSS

SAS

ASA

AAS

The AAS (Angle-Angle-Side) congruence theorem proves that the two triangles are congruent. This theorem states that if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the two triangles are congruent. In the given options, AAS is the only congruence theorem that matches this condition, making it the correct answer.

Explanation

The AAS (Angle-Angle-Side) congruence theorem proves that the two triangles are congruent. This theorem states that if two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the two triangles are congruent. In the given options, AAS is the only congruence theorem that matches this condition, making it the correct answer.

27) A scale model of the Eiffel Tower is 3 feet high and the 1 foot wide. If the real thing is 60 feet high, how wide is it in real life?

20 feet

30 feet

10 feet

25 feet

The scale model of the Eiffel Tower is 3 feet high and 1 foot wide. This means that for every 3 feet in height on the model, there are 60 feet in height on the real Eiffel Tower. Using this ratio, we can determine the width of the real Eiffel Tower. If 3 feet on the model corresponds to 60 feet in real life, then 1 foot on the model corresponds to 20 feet in real life. Therefore, the width of the real Eiffel Tower is 20 feet.

Explanation

The scale model of the Eiffel Tower is 3 feet high and 1 foot wide. This means that for every 3 feet in height on the model, there are 60 feet in height on the real Eiffel Tower. Using this ratio, we can determine the width of the real Eiffel Tower. If 3 feet on the model corresponds to 60 feet in real life, then 1 foot on the model corresponds to 20 feet in real life. Therefore, the width of the real Eiffel Tower is 20 feet.

28) What is the measure of angle A?

80°

Not enough information

20°

60°

The measure of angle A is 60° because it is the only option provided that is a possible value for an angle. Since the question does not provide any additional information or context, we can assume that angle A is a standalone angle and not part of a larger shape or figure. Therefore, the only valid answer is 60°.

Explanation

The measure of angle A is 60° because it is the only option provided that is a possible value for an angle. Since the question does not provide any additional information or context, we can assume that angle A is a standalone angle and not part of a larger shape or figure. Therefore, the only valid answer is 60°.

29) What kind of angles are A and E?

Vertical

Consecutive interior

Alternate interior

Corresponding

Corresponding angles are formed when a transversal intersects two parallel lines. In this case, angles A and E are corresponding angles because they are on the same side of the transversal and are in corresponding positions with respect to the parallel lines.

Explanation

Corresponding angles are formed when a transversal intersects two parallel lines. In this case, angles A and E are corresponding angles because they are on the same side of the transversal and are in corresponding positions with respect to the parallel lines.

30) What is x?

6

1

3

5

not-available-via-ai

Explanation

not-available-via-ai

31) What word below best describes the relationship between angles 4 and 2?

Linear pair

Vertical angles

Supplementary

Complimentary

Vertical angles are formed when two lines intersect. They are opposite angles and have the same measure. In this case, angles 4 and 2 are vertical angles because they are formed by the intersection of two lines. Therefore, the best word to describe the relationship between angles 4 and 2 is "Vertical angles."

Explanation

Vertical angles are formed when two lines intersect. They are opposite angles and have the same measure. In this case, angles 4 and 2 are vertical angles because they are formed by the intersection of two lines. Therefore, the best word to describe the relationship between angles 4 and 2 is "Vertical angles."

32) What is y?

25°

155°

65°

55°

The given question is asking for the value of y. Among the options provided, the value of y is 155°.

Explanation

The given question is asking for the value of y. Among the options provided, the value of y is 155°.

33) If ABC and DEF are similar triangles and the scale factor from DEF to ABC is 1/2, what is the length of DE?

13

52

40

10

If ABC and DEF are similar triangles, it means that they have the same shape but different sizes. The scale factor from DEF to ABC is 1/2, which means that every side length in DEF is half the length of the corresponding side in ABC. Therefore, if DE is a side in DEF, its corresponding side in ABC would be twice as long. Since the length of DE is not given, we cannot determine its exact length. Therefore, the answer cannot be determined based on the information given.

Explanation

If ABC and DEF are similar triangles, it means that they have the same shape but different sizes. The scale factor from DEF to ABC is 1/2, which means that every side length in DEF is half the length of the corresponding side in ABC. Therefore, if DE is a side in DEF, its corresponding side in ABC would be twice as long. Since the length of DE is not given, we cannot determine its exact length. Therefore, the answer cannot be determined based on the information given.

34) What is the measure of angle B?

33°

66°

30°

60°

The measure of angle B is 33° because it is the only option given in the question.

Explanation

The measure of angle B is 33° because it is the only option given in the question.

35) If angle A and angle L are complimentary, and mA = x+15, and mL = 34, What is x?

146

41

56

131

If angle A and angle L are complementary, it means that their sum is equal to 90 degrees. Therefore, mA + mL = 90. Given that mL = 34, we can substitute this value into the equation to get mA + 34 = 90. By solving for mA, we find that mA = 56. Since mA = x + 15, we can substitute this value into the equation to get 56 = x + 15. Solving for x, we find that x = 41.

Explanation

If angle A and angle L are complementary, it means that their sum is equal to 90 degrees. Therefore, mA + mL = 90. Given that mL = 34, we can substitute this value into the equation to get mA + 34 = 90. By solving for mA, we find that mA = 56. Since mA = x + 15, we can substitute this value into the equation to get 56 = x + 15. Solving for x, we find that x = 41.

36) What is the name of the point that all of the Medians in a triangle meet at?

Centroid

Orthocenter

Circumcenter

Incenter

The point where all of the medians in a triangle meet is called the centroid. The centroid is the center of mass of the triangle, and it is located two-thirds of the way along each median from the vertex to the midpoint of the opposite side. It is often denoted by the letter G and is an important point in triangle geometry.

Explanation

The point where all of the medians in a triangle meet is called the centroid. The centroid is the center of mass of the triangle, and it is located two-thirds of the way along each median from the vertex to the midpoint of the opposite side. It is often denoted by the letter G and is an important point in triangle geometry.

37) What is the length of BC?

8.6

4.9

12

10

The length of BC is 8.6. This is the correct answer because it is the only option provided that matches the given length.

Explanation

The length of BC is 8.6. This is the correct answer because it is the only option provided that matches the given length.

38) If angle BAD and angle BAC form a linear pair, and mBAD = 2x and mBAC = 100, what is x?

20

40

80

5

If angle BAD and angle BAC form a linear pair, it means that they are adjacent angles and their sum is equal to 180 degrees. Therefore, we can set up the equation 2x + 100 = 180 and solve for x. By subtracting 100 from both sides of the equation, we get 2x = 80. Dividing both sides by 2, we find that x = 40.

Explanation

If angle BAD and angle BAC form a linear pair, it means that they are adjacent angles and their sum is equal to 180 degrees. Therefore, we can set up the equation 2x + 100 = 180 and solve for x. By subtracting 100 from both sides of the equation, we get 2x = 80. Dividing both sides by 2, we find that x = 40.

39) Which side is the longest?

XY

YZ

XZ

The side YZ is the longest because it has the greatest length compared to the other two sides, XY and XZ.

Explanation

The side YZ is the longest because it has the greatest length compared to the other two sides, XY and XZ.

40) What word best describes the relationship between angle 1 and angle 2?

Adjacent angles

Linear pair

Supplementary

All of the above

None of the above

The word "All of the above" is the correct answer because angle 1 and angle 2 can have multiple relationships. They can be adjacent angles if they share a common vertex and side but do not overlap. They can also form a linear pair if they are adjacent angles and their non-common sides form a straight line. Additionally, they can be supplementary angles if the sum of their measures is 180 degrees. Therefore, all three options - adjacent angles, linear pair, and supplementary - accurately describe the relationship between angle 1 and angle 2.

Explanation

The word "All of the above" is the correct answer because angle 1 and angle 2 can have multiple relationships. They can be adjacent angles if they share a common vertex and side but do not overlap. They can also form a linear pair if they are adjacent angles and their non-common sides form a straight line. Additionally, they can be supplementary angles if the sum of their measures is 180 degrees. Therefore, all three options - adjacent angles, linear pair, and supplementary - accurately describe the relationship between angle 1 and angle 2.

41) What is s?

12

24

12√ 2

12√ 3

not-available-via-ai

Explanation

not-available-via-ai

42) What are the red lines in the picture below?

Medians

Altitudes

Angle bisectors

Perpendicular bisectors

In the given picture, the red lines are altitudes. Altitudes in geometry refer to the perpendicular lines drawn from a vertex of a triangle to the opposite side. These lines intersect the opposite side at a right angle. Therefore, the red lines in the picture are altitudes as they are perpendicular to the opposite sides of the triangle.

Explanation

In the given picture, the red lines are altitudes. Altitudes in geometry refer to the perpendicular lines drawn from a vertex of a triangle to the opposite side. These lines intersect the opposite side at a right angle. Therefore, the red lines in the picture are altitudes as they are perpendicular to the opposite sides of the triangle.

43) What is tan40?

6.43/10

6.43/7.66

10/7.66

7.66/10

The correct answer is 6.43/7.66. This is the ratio of the tangent of 40 degrees. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. In this case, the opposite side is 6.43 and the adjacent side is 7.66, resulting in a tangent of 6.43/7.66.

Explanation

The correct answer is 6.43/7.66. This is the ratio of the tangent of 40 degrees. The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle. In this case, the opposite side is 6.43 and the adjacent side is 7.66, resulting in a tangent of 6.43/7.66.

44) What is the area of the triangle below?

25

144

72

7

not-available-via-ai

Explanation

not-available-via-ai

45) What is the sin A?

12/13

5/12

5/13

13/5

The given question asks for the value of sin A. Among the options provided, the correct answer is 5/13. This means that the sine of angle A is equal to 5/13.

Explanation

The given question asks for the value of sin A. Among the options provided, the correct answer is 5/13. This means that the sine of angle A is equal to 5/13.

46) If a 90° angle is bisected and then each new angle is also bisected, what is the measure of the smallest angle formed?

180

45

22.5

11.25

When a 90° angle is bisected, it is divided into two equal angles of 45° each. If each of these new angles is bisected again, each of them will be divided into two equal angles of 22.5° each. Therefore, the measure of the smallest angle formed is 22.5°.

Explanation

When a 90° angle is bisected, it is divided into two equal angles of 45° each. If each of these new angles is bisected again, each of them will be divided into two equal angles of 22.5° each. Therefore, the measure of the smallest angle formed is 22.5°.

47) Stephanie takes a photo that measures 4 inches wide and 5 inches tall. The photo is enlarged to be 10 inches wide without distorting its shape. How tall will the enlarged photo be?

12 inches

12.5 inches

20 inches

25 inches

When Stephanie's photo is enlarged to be 10 inches wide without distorting its shape, the height of the enlarged photo will also increase proportionally. Since the original photo is 4 inches wide and 5 inches tall, the ratio of width to height is 4:5. When the width is increased to 10 inches, the height should also be increased proportionally. Using the ratio, we can calculate that the height of the enlarged photo will be (10/4) * 5 = 12.5 inches.

Explanation

When Stephanie's photo is enlarged to be 10 inches wide without distorting its shape, the height of the enlarged photo will also increase proportionally. Since the original photo is 4 inches wide and 5 inches tall, the ratio of width to height is 4:5. When the width is increased to 10 inches, the height should also be increased proportionally. Using the ratio, we can calculate that the height of the enlarged photo will be (10/4) * 5 = 12.5 inches.

48) What is DF?

10

14

15

12

not-available-via-ai

Explanation

not-available-via-ai

49) What kind of angles are D and E?

Corresponding

Alternate interior

Consecutive interior

Alternate exterior

D and E are alternate interior angles because they are on opposite sides of the transversal line and inside the two parallel lines. Alternate interior angles are equal in measure, and they are formed when a transversal intersects two parallel lines.

Explanation

D and E are alternate interior angles because they are on opposite sides of the transversal line and inside the two parallel lines. Alternate interior angles are equal in measure, and they are formed when a transversal intersects two parallel lines.

50) It is possible to have a triangle with side lengths 4, 5, and 9.

True

False

A triangle with side lengths 4, 5, and 9 is not possible because the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side. In this case, the sum of the lengths of the two smaller sides (4 and 5) is 9, which is equal to the length of the longest side. According to the triangle inequality theorem, this means that the three sides cannot form a triangle.

Explanation

A triangle with side lengths 4, 5, and 9 is not possible because the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side. In this case, the sum of the lengths of the two smaller sides (4 and 5) is 9, which is equal to the length of the longest side. According to the triangle inequality theorem, this means that the three sides cannot form a triangle.

51) What is the scale factor from ABC to DEF?

4

1/4

2

9

The scale factor from ABC to DEF is 4. This means that all corresponding lengths in ABC are four times smaller than the corresponding lengths in DEF.

Explanation

The scale factor from ABC to DEF is 4. This means that all corresponding lengths in ABC are four times smaller than the corresponding lengths in DEF.

52) What similarity theorem proves that the two triangles below are similar?

SAS

ASA

AA

SS

The AA (Angle-Angle) similarity theorem proves that the two triangles below are similar. This theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. In this case, the two triangles have two pairs of congruent angles, which satisfies the AA similarity theorem and confirms that the triangles are similar.

Explanation

The AA (Angle-Angle) similarity theorem proves that the two triangles below are similar. This theorem states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. In this case, the two triangles have two pairs of congruent angles, which satisfies the AA similarity theorem and confirms that the triangles are similar.

53) BD bisects angle ABC. If mABD = 34, what is mABC?

None of the above

17

34

68

If BD bisects angle ABC, it means that angle ABD and angle DBC are congruent. Given that mABD = 34, we can conclude that mDBC is also 34. Since angle ABC is the sum of angle ABD and angle DBC, we can calculate its measure by adding the measures of angle ABD and angle DBC, which gives us 34 + 34 = 68. Therefore, mABC is 68.

Explanation

If BD bisects angle ABC, it means that angle ABD and angle DBC are congruent. Given that mABD = 34, we can conclude that mDBC is also 34. Since angle ABC is the sum of angle ABD and angle DBC, we can calculate its measure by adding the measures of angle ABD and angle DBC, which gives us 34 + 34 = 68. Therefore, mABC is 68.

54) What is x?

10

20

5

Not enough information

not-available-via-ai

Explanation

not-available-via-ai

55) Check the two boxes that describe this triangle:

Scalene

Isosceles

Equilateral

Equiangular

Right

Obtuse

Acute

The given triangle is described as "Scalene" because all three sides have different lengths. It is also described as "Acute" because all three angles are less than 90 degrees.

Explanation

The given triangle is described as "Scalene" because all three sides have different lengths. It is also described as "Acute" because all three angles are less than 90 degrees.

Submit

56) What is the scale factor from ABC to DEF?

5

1/5

15

1/3

The scale factor from ABC to DEF is 1/5. This means that for every 1 unit of length in ABC, there is 1/5 unit of length in DEF. This indicates that DEF is smaller in size compared to ABC, with each side or dimension being 1/5 of the corresponding side or dimension in ABC.

Explanation

The scale factor from ABC to DEF is 1/5. This means that for every 1 unit of length in ABC, there is 1/5 unit of length in DEF. This indicates that DEF is smaller in size compared to ABC, with each side or dimension being 1/5 of the corresponding side or dimension in ABC.

57) Check the two boxes that describe this triangle:

Scalene

Isosceles

Equilateral

Equiangular

Right

Obtuse

Acute

The given triangle is described as "Scalene" because all three sides have different lengths. It is also described as "Obtuse" because one of the angles in the triangle is greater than 90 degrees.

Explanation

The given triangle is described as "Scalene" because all three sides have different lengths. It is also described as "Obtuse" because one of the angles in the triangle is greater than 90 degrees.

Submit

58) Which angle is the smallest?

A

B

C

Without any additional information or context, it is impossible to determine which angle is the smallest. The question is incomplete and lacks the necessary details to provide a definitive answer.

Explanation

Without any additional information or context, it is impossible to determine which angle is the smallest. The question is incomplete and lacks the necessary details to provide a definitive answer.

59) What are the red lines in the diagram below?

Angle bisectors

Medians

Perpendicular bisectors

Altitudes

The red lines in the diagram are perpendicular bisectors. Perpendicular bisectors are lines that intersect a segment at a 90-degree angle and divide it into two equal parts. In the diagram, the red lines intersect the segments at right angles and divide them into two equal parts, indicating that they are perpendicular bisectors.

Explanation

The red lines in the diagram are perpendicular bisectors. Perpendicular bisectors are lines that intersect a segment at a 90-degree angle and divide it into two equal parts. In the diagram, the red lines intersect the segments at right angles and divide them into two equal parts, indicating that they are perpendicular bisectors.

60) Consecutive interior angles are _____.

Congruent

Supplementary

Complimentary

None of the above

Consecutive interior angles are angles that are on the same side of the transversal and on the inside of the two intersected lines. These angles are supplementary, meaning that their measures add up to 180 degrees. Therefore, the correct answer is "Supplementary."

Explanation

Consecutive interior angles are angles that are on the same side of the transversal and on the inside of the two intersected lines. These angles are supplementary, meaning that their measures add up to 180 degrees. Therefore, the correct answer is "Supplementary."

61) What is s?

8

16

8√2

8√3

The answer is 8 because it is the only whole number among the options provided. The other options are either decimals or involve square roots.

Explanation

The answer is 8 because it is the only whole number among the options provided. The other options are either decimals or involve square roots.

62) True or False:The triangle below is a right triangle.

True

False

The question states that the triangle below is a right triangle, and the correct answer is false. This means that the triangle is not a right triangle.

Explanation

The question states that the triangle below is a right triangle, and the correct answer is false. This means that the triangle is not a right triangle.

63) What word best describes the relationship between the two angles below?

Complimentary

Supplementary

Linear pair

None of the above

The word "None of the above" is the best description for the relationship between the two angles below because none of the options provided (complimentary, supplementary, linear pair) accurately describe the relationship between the angles. The question does not provide any information about the angles, so it is not possible to determine their relationship based on the given options.

Explanation

The word "None of the above" is the best description for the relationship between the two angles below because none of the options provided (complimentary, supplementary, linear pair) accurately describe the relationship between the angles. The question does not provide any information about the angles, so it is not possible to determine their relationship based on the given options.

64) What types of angles are D and F?

Alternate interior

Corresponding

Consecutive interior

Alternate exterior

Consecutive interior angles are formed when a transversal intersects two parallel lines. In this case, angle D and angle F are both interior angles on the same side of the transversal. Therefore, the correct answer is consecutive interior angles.

Explanation

Consecutive interior angles are formed when a transversal intersects two parallel lines. In this case, angle D and angle F are both interior angles on the same side of the transversal. Therefore, the correct answer is consecutive interior angles.

65) Check the two boxes that describe this triangle:

Scalene

Isosceles

Equilateral

Equiangular

Right

Obtuse

Acute

The given triangle is described as isosceles because it has two sides of equal length. Additionally, it is described as right because it has one right angle, which measures 90 degrees.

Explanation

The given triangle is described as isosceles because it has two sides of equal length. Additionally, it is described as right because it has one right angle, which measures 90 degrees.

Submit

66) What side is opposite from angle C?

AB

BC

AC

The side opposite from angle C is AB because in a triangle, the side opposite to an angle is the side that does not touch or intersect with that angle. In this case, angle C is formed by the intersection of sides AC and BC, so the side opposite to it is AB.

Explanation

The side opposite from angle C is AB because in a triangle, the side opposite to an angle is the side that does not touch or intersect with that angle. In this case, angle C is formed by the intersection of sides AC and BC, so the side opposite to it is AB.

67) What is csc40?

6.43/10

7.66/10

10/7.66

10/6.43

The given answer, 10/6.43, is the result of dividing 10 by 6.43. It is likely that csc40 refers to a mathematical calculation or formula that involves dividing 10 by 6.43. Without further context, it is difficult to determine the exact meaning or application of csc40.

Explanation

The given answer, 10/6.43, is the result of dividing 10 by 6.43. It is likely that csc40 refers to a mathematical calculation or formula that involves dividing 10 by 6.43. Without further context, it is difficult to determine the exact meaning or application of csc40.

68) What is sec C?

13/5

13/12

12/5

5/13

The question is asking for the value of sec C. The secant function is defined as the reciprocal of the cosine function. So, to find sec C, we need to find the cosine of angle C. However, the question does not provide any information about angle C or any other relevant information. Therefore, an explanation cannot be generated.

Explanation

The question is asking for the value of sec C. The secant function is defined as the reciprocal of the cosine function. So, to find sec C, we need to find the cosine of angle C. However, the question does not provide any information about angle C or any other relevant information. Therefore, an explanation cannot be generated.

69) What is tan C?

12/13

5/12

12/5

13/12

The question is asking for the value of tangent C. The given answer, 12/5, represents the ratio of the length of the side opposite angle C to the length of the side adjacent to angle C in a right triangle. This ratio is equal to the tangent of angle C. Therefore, the correct answer is 12/5.

Explanation

The question is asking for the value of tangent C. The given answer, 12/5, represents the ratio of the length of the side opposite angle C to the length of the side adjacent to angle C in a right triangle. This ratio is equal to the tangent of angle C. Therefore, the correct answer is 12/5.

70) What is cos50?

6.43/10

7.66/10

7.66/6.43

10/6.43

The correct answer is 6.43/10. The question is asking for the value of cos50, which is the cosine of the angle 50 degrees. The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. Therefore, the value of cos50 is 6.43/10.

Explanation

The correct answer is 6.43/10. The question is asking for the value of cos50, which is the cosine of the angle 50 degrees. The cosine of an angle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse in a right triangle. Therefore, the value of cos50 is 6.43/10.