2016 Gauss 8 Problem 11

In the diagram, \triangle PQR is right-angled. Point S lies on PR so that \triangle QRS is equilateral and \triangle PQS is isosceles with PS = QS. The measure of \angle QPR is

\textbf{(A)}\ 35^\circ\quad \textbf{(B)}\ 37.5^\circ\quad \textbf{(C)}\ 25^\circ\quad \textbf{(D)}\ 32.5^\circ\quad \textbf{(E)}\ 30^\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 Gauss contests here.