Question

The trapezoids are similar. Both the left and right sides of the trapezoids are not parallel. Find the values of x, a, b, r° and s°. Explain your answers.

Answer 1

see explanation

Explanation:

Since the figures are similar then the ratios of corresponding sides are equal, that is

`(12)/(x)` =
`(9)/(6)` ( cross- multiply )

9x = 72 ⇒ x = 8

Also

`(a)/(5)` =
`(9)/(6)` ( cross- multiply )

6a = 45 ⇒ a = 7.5

And

`(b)/(7)` =
`(9)/(6)` ( cross- multiply )

6b = 63 ⇒ b = 10.5

Corresponding angles in the 2 figures are congruent, thus

∠s = 83°

Each lower base angle is supplementary to the upper base angle on the same side, hence

∠r = 180° - 30° = 150°