2018 Cayley Problem 15

In the diagram, \triangle PQS is equilateral. Also, \triangle PQR and \triangle PSR are isosceles with PQ = PR = PS. If \angle RPQ = \angle RPS, the measure of \angle QRS is

\textbf{(A)}\ 30^\circ\quad \textbf{(B)}\ 60^\circ\quad \textbf{(C)}\ 15^\circ\quad \textbf{(D)}\ 20^\circ\quad \textbf{(E)}\ 45^\circ

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Cayley contests here.