Five squares in a configuration. What’s the angle α?

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## Solution

The angle α is 45°.

Acknowledging the 135° angle at E, one gets the quarter circle centred in D. It is easy to see ΔAED is an equilateral triangle, as is ΔDGF. Thus we see that DNEC is a cyclic quadrilateral. Now using the Inscribed Angle Theorem one gets that α=∠NGE/2=45°.