If the measure of one of the interior angle of a regular polygon is 40° how many sides does the polygon have

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
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If the measure of one of the interior angle of a regular polygon is 40° how many sides does the polygon have?
Expert Solution
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Nine sides

If this is the exterior angle,then number of sides = 8 

If this is the interior angle then sides  come in ratio and number of sides can't come in ratio.

Every polygon's exterior angle sum equals 360.

 

A regular polygon is a flat shape whose sides are all equal and whose angles are all equal. The formula for finding the sum of the measure of the interior angles is (n - 2) * 180. To find the measure of one interior angle, we take that formula and divide by the number of sides n: (n - 2) * 180 / n.

 

 

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