Is it possible to have a regular polygon with measure of each exterior angle as 22°?

Question

Is it possible to have a regular polygon with measure of each exterior angle as 22&#xB0;?

Philoid · Accepted Answer

We know that the sum of all exterior angles of all polygons is 360^o.

And, in a regular polygon, each exterior angle is of the same measure.

Therefore, if 360^o is a perfect multiple of the given exterior angle, then the given polygon will be possible

Exterior angle = 22°

360^o is not a perfect multiple of 22^o.

Hence, such polygon is not possible