Question 739409

The sum of the measures of the exterior angles of a polygon, one at each vertex, is always {{{360}}}°.

When you have a regular polygon, all the exterior angles have the same measure, as long as you measure corresponding angles at each vertex. 
So, the angle measure in degrees = {{{360/n}}} where {{{n}}} the number of vertices in the polygon, and the number of vertices equals the number of {{{sides}}}.

examples:

1.

if the angle measure is, for example{{{30}}} degrees, the {{{360/n=30}}} => {{{360=30n}}}

=> {{{360/30=n}}}=> {{{12=n}}}; so, the polygon has 12 sides

or, 

2.

if the exterior angle measures {{{120}}} degrees, we will have

{{{360/n=120}}} => {{{360=120n}}}

=> {{{360/120=n}}}=> {{{3=n}}}; the polygon has {{{3}}} sides