Question
Find the number of sides in a regular polygon, when each interior angle is $: 135^\circ$
✓
Answer
Each interior angle of a regular polygon
$=\frac{(n-2) \times 180^{\circ}}{n}$
$\Rightarrow \frac{(n-2)^n \times 180^{\circ}}{n}=135^{\circ}$
$\Rightarrow 180^{\circ}(n-2)=135^{\circ}(n)$
$\Rightarrow 4(n-2)=3 n$
$\Rightarrow n=8 . $
$=\frac{(n-2) \times 180^{\circ}}{n}$
$\Rightarrow \frac{(n-2)^n \times 180^{\circ}}{n}=135^{\circ}$
$\Rightarrow 180^{\circ}(n-2)=135^{\circ}(n)$
$\Rightarrow 4(n-2)=3 n$
$\Rightarrow n=8 . $
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