SAT Question 585a9138: Lines, Angles, and Triangles answer and explanation with Desmos solution

It's given that triangles $ABC$ and $DEF$ are congruent with angle $A$ corresponding to angle $D$. Corresponding angles of congruent triangles are congruent and, therefore, have equal measure. It's given that the measure of angle $A$ is $27^{\circ }$. It follows that the measure of angle $D$ is also $27^{\circ }$. It's given that angle $E$ is a right angle. Therefore, the measure of angle $E$ is $90^{\circ }$. Let $x$ represent the measure, in degrees, of angle $F$. Since the measures of the angles in a triangle sum to $180^{\circ }$, it follows that $27+90+x=180$, or $117+x=180$. Subtracting $117$ from both sides of this equation yields $x=63$. Therefore, the measure, in degrees, of angle $F$ is $63$.