SAT Question 7268586c: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice D is correct. The sum of the angle measures of a triangle is $180^{\circ }$. It’s given that the measure of angle $Q$ is $132^{\circ }$, the measure of angle $P$ is $24^{\circ }$, and the measure of angle $R$ is $x^{\circ }$. It follows that $x+132+24=180$, or $x+152=180$. Subtracting $152$ from both sides of this equation yields $x=24$.

Alternate approach: It’s given that in the triangle shown, $PQ=QR$. Thus, triangle $PQR$ is an isosceles triangle. Since base angles of an isosceles triangle are congruent, the measure of angle $P$ is equal to the measure of angle $R$. Therefore, the measure of angle $R$ is $24^{\circ }$, and the value of $x$ is $24$.