SOLUTION: How many sides does a regular polygon have when each exterior angle measure is one eighth the measure of the interior angle?

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Question 258926: How many sides does a regular polygon have when each exterior angle measure is one eighth the measure of the interior angle?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
How many sides does a regular polygon have when each exterior angle measure is one eighth the measure of the interior angle?
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Let the interior be "x"
Then the exterior is (1/8)x
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Equation:
x + (1/8)x = 180
8x + x = 8*180
9x = 8*180
x = 8*20 = 160 degrees (measure of one of the interior angles)
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(1/8)x = (1/8)160 = 20 degrees (measure of one of the exterior angles)
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Fact: The sum of the exterior angles is 360
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Equation:
# of exterior angles = # of sides = 360/20 = 18
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Cheers,
Stan H.