In triangle X Y Z , angle Y is a right angle, point P lies on

The correct answer is $153$. Since it's given that $\overline{PQ}$ is parallel to $\overline{XY}$ and angle $Y$ is a right angle, angle $ZQP$ is also a right angle. Angle $ZPQ$ is complementary to angle $XZY$, which means its measure, in degrees, is $90-63$, or $27$. Since angle $XPQ$ is supplementary to angle $ZPQ$, its measure, in degrees, is $180-27$, or $153$.