# ABCDE is a regular pentagon. Calculate the magnitude of each angle of ?BED.

Given n=5

$\therefore$ Each interior angle =$\frac{(2n-4)\times90^{\circ}}{n}=\frac{(2\times5-4)\times90^{\circ}}{5}=108^{\circ}$

In ? ABE , ∠A=$108^{\circ}$ and AB=AE
$\Rightarrow \angle ABE=\angle AEB =\frac{180^{\circ}-108^{\circ}}{2}=36^{\circ}$
$\therefore \angle BED =\angle AED-\angle AEB=108^{\circ}-36^{\circ}=72^{\circ}$
Similarly, $\angle BDE=72^{\circ}$
and, $\angle EBD=180^{\circ}-(72+72)^{\circ}=36^{\circ}$

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