MathNet 2015-part-06 — 191 problems (EN–VI) Question 163

Trapezoid $ABCD$ with $BC \parallel AD$ is given. On the diagonals $AC$ and $BD$ there are points $P$ and $Q$ respectively, such that $AC$ bisects $\angle BPD$ and $BD$ bisects $\angle AQC$. Prove that $\angle BPD = \angle AQC$.