SOLUTION: The measure of each interior angle of a regular polygon is 11 times that of the exterior angle. How many sides does the polygon have?
I can solve this one by using the chart our
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Question 215232: The measure of each interior angle of a regular polygon is 11 times that of the exterior angle. How many sides does the polygon have?
I can solve this one by using the chart our teacher had us make, that calculates interior and exterior angles for several regular polygons. But is there also a mathematical way of solving this question?
Please explain.
Thank you!
Saskia
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The measure of each interior angle of a regular polygon is 11 times that of the exterior angle. How many sides does the polygon have?
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First find the interior angle.
The interior and exterior are supplementary, meaning they total 180 degs.
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I = 11*E
I + E = 180
11E + E = 180
E = 15 degs
I = 165 degs
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Then, the total of all interior angles of a polygon is 180*(n-2) where n is the # of sides and angles.
I = Total of angles/# of angles
I = 180*(n-2)/n = 165
165n = 180n - 360
-15n = -360
n = 24
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