SOLUTION: if Each exterior angle of a regular polygon is 10 degrees how many sides does the polygon have?

Question 844606: if Each exterior angle of a regular polygon is 10 degrees how many sides does the polygon have?

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
As you go around a polygon, you have to change course by a certain angle at each vertex. That angle is the exterior angle.

If at each vertex you have to veer right by ,
by the time you have turned the nth vertex you will be facing in the same direction as when you started.
Any snowboarder will tell you that when you have turned around once and end up facing in the same direction, you have changed direction by a total angle of .
Your teacher will tell you that you have to remember what was taught in geometry class, but snowboarders know geometry without studying it. So do gardeners, carpenters, and mechanics. They may not be able to recite that the sum of the measures of the exterior angles of a polygon is , but they know it in a way they can use that knowledge.
So , and solving for we find
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