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Geometry and Trigonometry / Lines, angles, and triangles Difficulty: Hard

In triangle $X Y Z$ , angle $Y$ is a right angle, point $P$ lies on $\bar{X Z}$ , and point $Q$ lies on $\bar{Y Z}$ such that $\bar{P Q}$ is parallel to $\bar{X Y}$ . If the measure of angle $X Z Y$ is $63 degree$ , what is the measure, in degrees, of angle $X P Q$ ?

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Explanation

The correct answer is $153$ . Since it's given that $\bar{P Q}$ is parallel to $\bar{X Y}$ and angle $Y$ is a right angle, angle $Z Q P$ is also a right angle. Angle $Z P Q$ is complementary to angle $X Z Y$ , which means its measure, in degrees, is $90 minus 63$ , or $27$ . Since angle $X P Q$ is supplementary to angle $Z P Q$ , its measure, in degrees, is $180 minus 27$ , or $153$ .