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The spinning top

An equilateral triangle stacked on a pentagon. What’s the angle?

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Solution

The angle is 48°.

First we recognise the isosceles triangle EDF. It has a top angle of 108°+60°=168°. From the interior angle sum we deduce that the two other angles must be 6°.

From reflection symmetry in the line through F it is seen that α + 2*6°=60°. Hence α = 48°.

Visual solution

Visual solution by David Andriana.
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