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.
