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MathNet 2008-part-01 — 165 problems (EN–VI) Question 158

Math Olympiad Vault · MathNet 2008-part-01 — 165 problems (EN–VI)

Question 158

Given is a (general) trapezoid $ABCD$ whose diagonals meet at the point $P$. A point $Q$ lies between the parallels $AB$ and $DC$ such that $\angle AQB = \angle CQD$ holds and the line $BC$ runs between $P$ and $Q$.
Prove that $\angle DQP = \angle BAQ$ holds.