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UKMT Junior Kangaroo, 2018

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

In the triangle $PQR$ , the lengths of sides $PQ$ and $PR$ are the same. The point $S$ lies on $QR$ so that $QS = PS$ and $\angle RPS = 75^{\circ}$ . What is the size of $\angle QRP$ ?

(A) $35^{\circ}$ (B) $30^{\circ}$ (C) $25^{\circ}$ (D) $20^{\circ}$ (E) $15^{\circ}$

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