Question

Find the value of x in the trapezoid below. Show equations and all work that leads to your answer.

Answer 1

x = 21.5

Explanation:

In the given trapezoid, the angles are consecutive interior angles.

i.e, consider the parallel sides of a trapezoid as parallel lines and the common side as the transversal. So, it is parallel lines cut by a transversal make a pair of consecutive interior angles which are supplementary.

i.e,

(5x + 13)° + (3x - 5)° =180°

5x + 13 + 3x - 5 = 180

8x + 8 = 180

8x = 180 - 8 =172

x= 172/8 = 21.5

So, 5x + 13 = 5(21.5) + 13 = 120.5°

3x - 5 = 3(21.5) -5 = 59.5°