Angle & Triangle Quiz (7.G.5 & 7.G.2)

The measure of angle x is 99 degrees because it is stated in the question that the blue angle is 99 degrees, and angle x is the same as the blue angle.

A right angle is a type of angle that measures exactly 90 degrees. It is formed when two lines intersect each other perpendicular to each other. The other options, such as a straight angle, acute angle, and angle, do not have a specific measure of 90 degrees. A straight angle measures 180 degrees, an acute angle measures less than 90 degrees, and an angle is a general term that can refer to any measure of degrees. Therefore, the correct answer is right angle.

An obtuse angle is an angle that measures greater than 90 degrees but less than 180 degrees. It is larger than a right angle, which measures exactly 90 degrees, and smaller than a straight angle, which measures exactly 180 degrees.

An acute angle is an angle that measures less than 90 degrees. It is smaller than a right angle (90 degrees) and a straight angle (180 degrees), and larger than an obtuse angle (greater than 90 degrees). In other words, an acute angle is a sharp angle that is less than a quarter turn.

The question states that angle QPS is a right angle and angle RPS measures 16 degrees. Since angle QPS is a right angle, it measures 90 degrees. Therefore, angle QPR is the difference between angle QPS and angle RPS, which is 90 - 16 = 74 degrees.

A straight angle is formed when two rays lie on the same line and create a straight line. It measures exactly 180 degrees, making it the largest possible angle. This angle is often represented by a straight line with a small arc in the middle. It is called a straight angle because it forms a straight line.

The measure of angle x is 116 degrees because the given information states that the blue angle is 116 degrees, and angle x is the same as the blue angle.

The measure of angle LOM can be determined by subtracting the measure of angle MON from the measure of angle LON. Given that m

Since angle QPS is a right angle, it measures 90 degrees. Given that angle QPR measures 48 degrees, we can subtract this from 90 degrees to find angle RPS. Therefore, angle RPS measures 42 degrees.

Supplementary angles are two angles whose measures add up to 180 degrees. This means that when the measures of two angles are added together, the sum will always be 180 degrees. Therefore, the correct answer is "supplementary angles".

An angle is a figure formed by two rays with a common endpoint. It consists of two arms, which are the rays, and a vertex, which is the common endpoint. The rays extend indefinitely in opposite directions, creating the shape of an angle.

Adjacent angles are two angles that share a common vertex and a common side, but do not have any points in their interiors. In other words, they are side by side and do not overlap.

Vertical angles are formed when two lines intersect. They are opposite each other and share a common vertex. These angles have equal measures and are congruent. In other words, if one angle measures x degrees, then its vertical angle will also measure x degrees. Vertical angles are important in geometry and are used to solve various problems involving angles and lines.

Congruent angles are angles that have the same measure. This means that the angles are equal in size and can be superimposed on each other. When two angles are congruent, their measures are equal, and they have the same shape and orientation. Therefore, congruent angles can be considered identical.

This statement is true because there are certain measurements, such as having three sides of different lengths, where it is possible to form exactly two triangles. In such cases, the triangle inequality theorem is satisfied, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. This allows for the formation of two distinct triangles.

Complementary angles are two angles whose measures add up to 90 degrees. In other words, when you add the measures of two complementary angles, the sum will always be 90 degrees.

The sum of the angles in a triangle is always 180 degrees. In the first three sets of angles, the sum of the angles is 180 degrees, so they can form a triangle. However, in the last set of angles, the sum is 180 degrees, so they cannot form a triangle.

In order for a set of lengths to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. If we add the lengths of the sides in each set, we can see that only the set 16 feet, 14 feet, 4 feet satisfies this condition. Therefore, this set can form exactly one triangle.

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In the given options, none of the sets of lengths satisfy this condition. For example, in the first option, the sum of the lengths of the two shorter sides (6 inches and 2 inches) is less than the length of the longest side (8 inches), violating the triangle inequality theorem. Therefore, none of the given sets of lengths can form exactly one triangle.

None of the given sets of angles will form exactly one triangle. In order to form a triangle, the sum of the measures of any two angles must be greater than the measure of the third angle. However, in the given sets of angles, this condition is not satisfied. For example, in the set of angles 90°, 50°, 40°, the sum of the measures of the two smaller angles (50° + 40° = 90°) is equal to the measure of the largest angle (90°), which means that the angles cannot form a triangle. The same reasoning can be applied to the other sets of angles as well.