2018 Pascal Problem 18

In the diagram, \triangle PQR has \angle PQR = 120^\circ. Also, \angle QPS = \angle RPS and \angle QRS = \angle PRS. (In other words, SP and SR bisect \angle QPR and \angle QRP, respectively.) What is the measure of \angle PSR?

\textbf{(A)}\ 130^\circ\quad \textbf{(B)}\ 120^\circ\quad \textbf{(C)}\ 140^\circ\quad \textbf{(D)}\ 160^\circ\quad \textbf{(E)}\ 150^\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 Pascal contests here.