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

Answer:

see explanation

Step-by-step explanation:

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

$\frac{12}{x}$ = $\frac{9}{6}$ ( cross- multiply )

9x = 72 ⇒ x = 8

Also

$\frac{a}{5}$ = $\frac{9}{6}$ ( cross- multiply )

6a = 45 ⇒ a = 7.5

And

$\frac{b}{7}$ = $\frac{9}{6}$ ( 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°