Let $ABCD$ be a convex quadrilateral. Lines $AB$ and $CD$ meet at $P$, and lines $AD$ and $BC$ meet at $Q$. Let $O$ be a point in the interior of $ABCD$ such that $\angle BOP = \angle DOQ$. Prove that $\angle AOB +\angle COD = 180$.
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Let $ABCD$ be a convex quadrilateral. Lines $AB$ and $CD$ meet at $P$, and lines $AD$ and $BC$ meet at $Q$. Let $O$ be a point in the interior of $ABCD$ such that $\angle BOP = \angle DOQ$. Prove that $\angle AOB +\angle COD = 180$.