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.

see explanation

Step-by-step explanation:

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

= ( cross- multiply )

9x = 72 ⇒ x = 8

Also

= ( cross- multiply )

6a = 45 ⇒ a = 7.5

And

= ( 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°

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

source