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UKMT Junior Mathematical Challenge, 2018

Geometry Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

The diagram shows a quadrilateral $PQRS$ in which $PQ$ and $QR$ have the same length. Also $PR$ bisects $\angle SPQ$ , the ratio of $\angle SPR$ to $\angle PRS$ is $2 : 3$ and $\angle PSR = 110^{\circ}$ . How large is angle $PQR$ ?

(A) $124^{\circ}$ (B) $120^{\circ}$ (C) $110^{\circ}$ (D) $90^{\circ}$ (E) $28^{\circ}$

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