1954 AMC 12 Question 37

Question 37

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

1. $\angle m=\dfrac12(\angle p-\angle q)$
2. $\angle m=\dfrac12(\angle p+\angle q)$
3. $\angle d=\dfrac12(\angle q+\angle p)$
4. $\angle d=\dfrac12\angle m$
5. none of these is correct