SAT Question 014edcb7: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice B is correct. In the figure shown, since $\overline{QS}$ is a line segment, the sum of the measures of $\angle PRS$ and $\angle PRQ$ is $180^{\circ }$. It's given that the measure of $\angle PRS$ is $163^{\circ }$. Thus, the measure of $\angle PRQ$ is $(180-163{)}^{\circ }$, or $17^{\circ }$. The sum of the measures of the interior angles of a triangle is $180^{\circ }$. It's given that the measure of $\angle PQR$ is $132^{\circ }$. Therefore, the measure of $\angle QPR$ is $(180-17-132{)}^{\circ }$, or $31^{\circ }$.