MathNet 2000 — Math Olympiad Vault Question 99

In a convex quadrilateral $P Q R S$, $P Q = R S$, $(\sqrt{3}+1) Q R = S P$ and $\angle R S P - \angle S P Q = 30^{\circ}$. Prove that
$$
\angle P Q R - \angle Q R S = 90^{\circ}
$$