# If the measure of exterior angle of a regular polygon is 1/5 times its interior angle, how many sides does the polygon has?

Apr 11, 2017

Polygon has $12$ sides - it is dodecagon.

#### Explanation:

As the measure of the exterior angles of a regular polygon are $\frac{1}{5}$ times the measure of its interior angles,

each exterior angle of the regular polygon too will be $\frac{1}{5}$ times the measure of its interior angle.

Let the exterior angle be $x$ and then interior angle would be $5 x$

and as their sum is always ${180}^{\circ}$, we have

$x + 5 x = {180}^{\circ}$ or $6 x = {180}^{\circ}$ i.e. $x = \frac{180}{6} = {30}^{\circ}$

Now as sum of exterior angles of a polygon is always 360^

we have $\frac{{360}^{\circ}}{{30}^{\circ}} = 12$ exterior or interior angles i.e.

Polygon has $12$ sides - it is dodecagon.