SAT Question 322a6dfe: Lines, Angles, and Triangles answer and explanation with Desmos solution

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