SAT Question d5f349b7: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice B is correct. In similar triangles, corresponding angles are congruent. It's given that right triangles $PQR$ and $STU$ are similar, where angle $P$ corresponds to angle $S$. It follows that angle $P$ is congruent to angle $S$. In the triangles shown, angle $R$ and angle $U$ are both marked as right angles, so angle $R$ and angle $U$ are corresponding angles. It follows that angle $Q$ and angle $T$ are corresponding angles, and thus, angle $Q$ is congruent to angle $T$. It's given that the measure of angle $Q$ is $18^{\circ }$, so the measure of angle $T$ is also $18^{\circ }$. Angle $U$ is a right angle, so the measure of angle $U$ is $90^{\circ }$. The sum of the measures of the interior angles of a triangle is $180^{\circ }$. Thus, the sum of the measures of the interior angles of triangle $STU$ is $180$ degrees. Let $s$ represent the measure, in degrees, of angle $S$. It follows that $s+18+90=180$, or $s+108=180$. Subtracting $108$ from both sides of this equation yields $s=72$. Therefore, if the measure of angle $Q$ is $18$ degrees, then the measure of angle $S$ is $72$ degrees.