How to calculate the number of side of a polygon?

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I stuck on this problem. Please suggest any hint on how to solve this problem. Thanks in advance.

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Hint: What is $ \angle BEA + \angle CAE $?
Express that in 2 different ways.

$\angle BAE = \frac{360^\circ}{n} $

$\angle BEA + \angle CAE = 45^\circ $

$\frac{1}{n} + \frac{ 2}{n} = \frac{ 180^\circ}{ 45^\circ }$