SOLUTION: Hi, I was wondering, if the measure of each angle (the book does not state if the angle is interior or exterior) of a regular polygon is 120 degrees. Then how many sides does the p

Question 228025: Hi, I was wondering, if the measure of each angle (the book does not state if the angle is interior or exterior) of a regular polygon is 120 degrees. Then how many sides does the polygon have? If you could provide the answer as well as how you solved it that would be greatly appreciated. Thank you.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Hi, I was wondering, if the measure of each angle (the book does not state if the angle is interior or exterior) of a regular polygon is 120 degrees. Then how many sides does the polygon have? If you could provide the answer as well as how you solved it that would be greatly appreciated
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The sum of the interior angles of a polygon with n sides is:
180*(n-2)
Each angle is 180*(n-2)/n
180*(n-2)/n = 120
180n - 360 = 120n
60n = 360
n = 6
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If 120 is the exterior angle, then the interior angle = 60�
That's a triangle.
You can confirm that by using the method above.
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