SOLUTION: the measure of each interior angle of a regular polygon is 14 times the measure of an exterior angle. how many sides does the polygon have?

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Question 336962: the measure of each interior angle of a regular polygon is 14 times the measure of an exterior angle. how many sides does the polygon have?
Answer by stanbon(75887) About Me  (Show Source):
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the measure of each interior angle of a regular polygon is 14 times the measure of an exterior angle. how many sides does the polygon have?
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The interior and its corresponding exterior angle are supplementary.
x + 14x = 180
15x = 180
x = 12 degrees (the exterior angle)
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Fact: The sum of the exterior angles is 360 degrees
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# of exterior angles = 360/12 = 30
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# of sides = # of exterior angles = 30
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Cheers,
Stan H.