CONO-SUR 2018 Problem 1

Let $ABCD$ be a convex quadrilateral, where $R$ and $S$ are points in $DC$ and $AB$ , respectively, such that $AD=RC$ and $BC=SA$ . Let $P$ , $Q$ and $M$ be the midpoints of $RD$ , $BS$ and $CA$ , respectively. If $\angle MPC + \angle MQA = 90$ , prove that $ABCD$ is cyclic.