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question 2
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which angle property proves <pyd = 90°?
select one:
a. alternate exterior angles
b. supplementary angles
c. alternate interior angles
d. corresponding angles

Explanation:

The right - angle symbol at $\angle PYW$ indicates that $\angle PYW = 90^{\circ}$. Since $\angle PYD$ and $\angle PYW$ are the same angle (as they are the same geometric entity), $\angle PYD=90^{\circ}$ by the definition of a right - angle (a right - angle is defined as an angle of $90^{\circ}$), not by any of the angle relationships given in the options. But if we assume the question is about the general concept of identifying a $90^{\circ}$ angle among angle - relationship concepts, none of the angle relationships (alternate exterior, supplementary, alternate interior, corresponding) directly prove an angle is $90^{\circ}$. However, if we consider the context of perpendicular lines (which is related to right - angles), and assume some unstated perpendicularity situation, we note that supplementary angles add up to $180^{\circ}$. If we had a situation where an angle and $\angle PYD$ were supplementary and the other angle was $90^{\circ}$, then $\angle PYD$ would be $90^{\circ}$ by the supplementary - angle property.

Answer:

b. supplementary angles