SAT Question 95ca2683: Lines, Angles, and Triangles answer and explanation with Desmos solution

Choice C is correct. The sum of the interior angles of a triangle is $180^{\circ }$. It's given that the interior angles of triangle $ABC$ are $54^{\circ }$, $90^{\circ }$, and ${\left(\frac{k}{2}\right)}^{\circ }$. It follows that $54+90+\frac{k}{2}=180$, or $144+\frac{k}{2}=180$. Subtracting $144$ from each side of this equation yields $\frac{k}{2}=36$. Multiplying each side of this equation by $2$ yields $k=72$. Therefore, the value of $k$ is $72$.