Question

Find the exterior angle (in degree) of 8 sided regular polygon.

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Answer 1

Exterior angle of any regular polygon

= ${180}^{\circ }$ - interior angle

Interior angle of a regular polygon

= $\frac{(n-2)\times {180}^{\circ }}{n}$

Here, n=8

interior angle = $\frac{(8-2)}{8}\times 180={135}^{\circ }$

Exterior angle of regular polygon = ${180}^{\circ }$ - interior angle

= ${180}^{\circ }$ - ${135}^{\circ }$ = ${45}^{\circ }$

In general for n sided regular polygon

Exterior angle = ${180}^{\circ }$ - $\frac{(n-2)\times {180}^{\circ }}{n}$

= ${180}^{\circ }$ $\left[\frac{n-(n-2)}{n}\right]$

= ${180}^{\circ }$ $\times$ $\frac{2}{n}$ = $\frac{{360}^{\circ }}{n}$

So, exterior angle of n side regular polygon

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