MathNet 2019-part-02 — 184 problems (EN–VI) Question 169

Let $ABCD$ be a trapezoid such that $(AB)$ is parallel to $(CD)$. Let $P$ be a point of $[AC]$ and $Q$ a point of $[BD]$ such that $\widehat{APD} = \widehat{BQC}$.

Prove that $\widehat{AQD} = \widehat{BPC}$.