In the diagram, $\triangle P Q R$ is right-angled at $Q$ and has $\angle Q P R=54^{\circ}$. Also, point $S$ lies on $P Q$ such that $\angle P R S=\angle Q R S$. What is the measure of $\angle R S Q$ ?
(A) $36^{\circ}$
(B) $54^{\circ}$
(C) $108^{\circ}$
(D) $18^{\circ}$
(E) $72^{\circ}$

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-015.jpg?height=339&width=396&top_left_y=1088&top_left_x=1298)
Since $\triangle P Q R$ is right-angled at $Q$, then $\angle P R Q=90^{\circ}-\angle Q P R=90^{\circ}-54^{\circ}=36^{\circ}$.

Since $\angle P R S=\angle Q R S$, then $\angle Q R S=\frac{1}{2} \angle P R Q=\frac{1}{2}\left(36^{\circ}\right)=18^{\circ}$.

Since $\triangle R Q S$ is right-angled at $Q$, then $\angle R S Q=90^{\circ}-\angle Q R S=90^{\circ}-18^{\circ}=72^{\circ}$.

ANSWER: (E)