Angles inside regular polygons can usually be calculated by splitting the polygon into triangles around the centre. Split the regular pentagon into triangles. Each angle at the centre is \(72^\circ\) ...

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A tangent meets a circle at one point and one point only. The angle between a tangent and a radius is a right angle of \(90^\circ\). PT is a tangent and CT is a radius, therefore \(\angle CTP=90^\circ ...