1954 AHSME Problem 37

Given \triangle PQR with \overline{RS} bisecting \angle R, PQ extended to D and \angle n a right angle, then:

\textbf{(A)}\ \angle m = \frac {1}{2}(\angle p - \angle q) \qquad \textbf{(B)}\ \angle m = \frac {1}{2}(\angle p + \angle q) \textbf{(C)}\ \angle d =\frac{1}{2}(\angle q+\angle p)\qquad \textbf{(D)}\ \angle d =\frac{1}{2}\angle m\qquad \textbf{(E)}\ \text{none of these is correct}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.