Let $ \overline{\mathrm{PQ}} $ be the perpendicular to the line segment $ \overline{\mathrm{XY}} $. Let $ \overline{\mathrm{PQ}} $ and $ \overline{\mathrm{XY}} $ intersect in the point $ \mathrm{A} $. What is the measure of $ \angle \mathrm{PAY} $ ?

Given:

\( \overline{\mathrm{PQ}} \) is perpendicular to the line segment \( \overline{\mathrm{XY}} \).

\( \overline{\mathrm{PQ}} \) and \( \overline{\mathrm{XY}} \) intersect in the point \( \mathrm{A} \).

To do:

We have to find the measure of \( \angle \mathrm{PAY} \).
 Solution:

From the figure,

The measure of \( \angle \mathrm{PAY} \) is $90^o$.