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

Quadrilaterals $P Q R S$ and $W X Y Z$ are similar, where $P$ , $Q$ , and $R$ correspond to $W$ , $X$ , and $Y$ , respectively. The measure of $∠ S$ is $135 degree$ , $upper P upper S equals 45$ , and $upper W upper Z equals 9$ . What is the measure of $∠ Z$ ?

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Explanation

Choice D is correct. Corresponding angles in similar figures have equal measure. It's given that quadrilaterals $P Q R S$ and $W X Y Z$ are similar and that $P$ , $Q$ , and $R$ correspond to $W$ , $X$ , and $Y$ . It follows that $∠ S$ corresponds to $∠ Z$ . It's also given that the measure of $∠ S$ is $135 degree$ . Therefore, the measure of $∠ Z$ is $135 degree$ .

Choice A is incorrect and may result from conceptual errors.

Choice B is incorrect and may result from conceptual errors.

Choice C is incorrect. This is the supplement of the measure of $∠ Z$ , not the measure of $∠ Z$ .