Each exterior angle of a regular polygon measures 8 degrees. How many sides does the polygon have? Show your work!
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Answer:
The sum of the exterior angles of a regular polygon is 360, so if an exterior angle = 8, then the number of sides is 360/8 = 45.
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Interior and exterior angles are supplementary. In the ratio 8:1 the 180 degrees breaks down 160:20. Since the exterior angles always sum to 360, the 20 degree exterior angles imply 20 x 18 sides = 360 degrees. So there are 18 sides.
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