Lesson 3-2 Angles And Parallel Lines Video Quiz

Since a || b, we can conclude that the angle formed by m18 is equal to the angle formed by m22. Therefore, m22 must also be equal to 42.

Since a and b are parallel lines, the alternate interior angles are congruent. Therefore, m18 and m25 are congruent. Given that m18 is 42, it follows that m25 is also 42.

Since the area of each tile is represented by m2, and it is given that m2 = 125, we can conclude that each tile has an area of 125 square units. Therefore, the area of four tiles, represented by m4, would be 4 times the area of one tile, which is 125. Therefore, m4 = 4 * 125 = 500. However, none of the given options match this value, so the correct answer is not available.

To find the value of x, we need to equate m1, m2, and m3. From the given equations, we have:
9x + 6 = 2(5x - 3)
Expanding the brackets:
9x + 6 = 10x - 6
Rearranging the equation:
9x - 10x = -6 - 6
Simplifying:
-x = -12
Multiplying both sides by -1 to isolate x:
x = 12
Therefore, the correct answer is x = 12.

To find the value of y, we need to equate m3 to 20. Given that m3 = 5y + 14, we can set up the equation 5y + 14 = 20. Solving for y, we subtract 14 from both sides to get 5y = 6. Dividing both sides by 5, we find that y = 20.