UKMT Pink Kangaroo, 2020

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

A zig-zag line starts at the point $P$ , at one end of the diameter $PQ$ of a circle. Each of the angles between the zig-zag line and the diameter $PQ$ is equal to $\alpha$ as shown. After four peaks, the zig-zag line ends at the point $Q$ . What is the size of angle $\alpha$ ?

(A) $60^\circ$ (B) $72^\circ$ (C) $75^\circ$ (D) $80^\circ$ (E) $86^\circ$

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