Question 739409: How can I find the number of sides of a polygon when given only one exterior angle?
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!
The sum of the measures of the exterior angles of a polygon, one at each vertex, is always  °.
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 =  where  the number of vertices in the polygon, and the number of vertices equals the number of  .
examples:
1.
if the angle measure is, for example degrees, the  => 
=>  =>  ; so, the polygon has 12 sides
or,
2.
if the exterior angle measures  degrees, we will have
 => 
=>  =>  ; the polygon has  sides
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