If the measure of exterior angle of a regular polygon is $\frac{1}{5}$ $1/5$ times its interior angle, how many sides does the polygon has?

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Answer 1 · 2017-04-11T07:08:44

Polygon has $12$ $12$ sides - it is dodecagon.

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

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

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

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

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

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

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

Polygon has $12$ $12$ sides - it is dodecagon.

If the measure of exterior angle of a regular polygon is 1/5151/5 times its interior angle, how many sides does the polygon has?