SAT Question c7bed21d: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice B is correct. It's given that quadrilateral $P^{{}^{\prime }}{Q}^{{}^{\prime }}{R}^{{}^{\prime }}{S}^{{}^{\prime }}$ is similar to quadrilateral $PQRS$, where $P$, $Q$, $R$, and $S$ correspond to $P^{{}^{\prime }}$, $Q^{{}^{\prime }}$, $R^{{}^{\prime }}$, and $S^{{}^{\prime }}$, respectively. Since corresponding angles of similar quadrilaterals are congruent, it follows that the measure of angle $P$ is equal to the measure of angle $P^{{}^{\prime }}$. It's given that the measure of angle $P$ is $30^{\circ }$. Therefore, the measure of angle $P^{{}^{\prime }}$ is $30^{\circ }$.