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UKMT Intermediate Mathematical Challenge, 2017

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

In the diagram shown, $PQ = SQ = QR$ and $\angle SPQ = 2 \times \angle RSQ$ . What is the size of angle $QRS$ ?

(A) $20^\circ$ (B) $25^\circ$ (C) $30^\circ$ (D) $35^\circ$ (E) $40^\circ$

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