Question

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

Answer 1

Polygon has `12` sides - it is dodecagon.

Explanation:

As the measure of the exterior angles of a regular polygon are `1/5` times the measure of its interior angles,

each exterior angle of the regular polygon too will be `1/5` times the measure of its interior angle.

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

and as their sum is always `180^@`, we have

`x+5x=180^@` or `6x=180^@` i.e. `x=180/6=30^@`

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

we have `(360^@)/(30^@)=12` exterior or interior angles i.e.

Polygon has `12` sides - it is dodecagon.