SAT Question 0bb39de4: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice B is correct. It's given that triangle $ABC$ is congruent to triangle $DEF$. Corresponding angles of congruent triangles are congruent and, therefore, have equal measure. It's given that angle $A$ corresponds to angle $D$, and that the measure of angle $A$ is $18^{\circ }$. It's also given that the measures of angles $B$ and $E$ are $90^{\circ }$. Since these angles have equal measure, they are corresponding angles. It follows that angle $C$ corresponds to angle $F$. Let $x^{\circ }$ represent the measure of angle $C$. Since the sum of the measures of the interior angles of a triangle is $180^{\circ }$, it follows that $18^{\circ }+90^{\circ }+x^{\circ }=180^{\circ }$, or $108^{\circ }+x^{\circ }=180^{\circ }$. Subtracting $108^{\circ }$ from both sides of this equation yields $x^{\circ }=72^{\circ }$. Therefore, the measure of angle $C$ is $72^{\circ }$. Since angle $C$ corresponds to angle $F$, it follows that the measure of angle $F$ is also $72^{\circ }$.