$PQRS$ is a parallelogram and $TSR$ is a straight line. Find the values of $p$ and $q$ in th

Question

$PQRS$ is a parallelogram and $TSR$ is a straight line. Find the values of $p$ and $q$ in the diagram below, stating your reasons clearly. Source consistency note: Let $O$ be the intersection of the diagonals. The exact angle labels are inconsistent: triangle $PQO$ gives $PO/QO=\sin40^\circ/\sin52^\circ$, while triangle $RQO$ gives $RO/QO=\sin38^\circ/\sin50^\circ$. These are unequal, contradicting $PO=RO$ in a parallelogram. The numerical answers below are conditional angle-chasing results, not angles of a figure satisfying every label.

Accepted Answer

$p=88,\ q=50$. The results are conditional; the exact source labels conflict.

Angles in a Parallelogram with a Straight Line

Angles in a Parallelogram with a Straight Line

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