Question

What are the respective values of x, y, and z for parallelogram ABCD?

A . 56.31°, 67.38°, 67.38°

B. 67.38°, 33.69°, 67.38°

C. 28.15°, 56.31°, 33.69°

D. 56.31°, 56.31°, 67.38°

Answer 1

56.31°, 56.31°, 67.38°

Explanation:

Answer 2

The interior angles of triangle BCD must add up to 180 degrees, so


`z+2*56.31=180\implies z=67.38`

Angles BAD and BCD are congruent (since this is a parallelogram) so
`x=56.31`.

Also because this is a parallelogram, the triangles BCD and ACD are congruent, so angles ABD and CBD are congruent, which means
`y=56.31`.

That leads to the answer of (D)