Question

Given the figure below is a special type of trapezoid and WX || YZ, which angle pairs can be proven supplementary by the given information? Select all that apply.

∠W and ∠Z
∠W and ∠Y
∠X and ∠Y
∠X and ∠Z
∠W and ∠X

Answer 1

The answer:

<W and <Z

<X and <Y

<W and <X

Explanation:

Answer 2

Answer: The correct options are

(A) ∠W and ∠Z

(C) ∠X and ∠Y.

Step-by-step explanation: Given that the figure is a special type of trapezoid and WX || YZ.

We are to select all the angle pairs that can be proven supplementary by the given information.

We know that

if two parallel lines are cut by a transversal, then the sum of the measures of interior angles on the same side of the transversal is 180°.

In the given trapezoid, we have

WX || YZ and WZ is a transversal, so ∠W and ∠Z are interior angles on the same side of the transversal WZ.

So,

m∠W + m∠Z = 180°.

This implies that ∠W and ∠Z are supplementary.

Similarly,

WX || YZ and XY is a transversal, so ∠X and ∠Y are interior angles on the same side of the transversal XY.

So,

m∠X + m∠Y = 180°.

This implies that ∠X and ∠Y are supplementary.

Therefore, the pairs of angles that can be proven supplementary with the given information are

∠W and ∠Z ; ∠X and ∠Y.

Thus, (A) and (C) are correct options.