SOLUTION: The Measure of each interior angle of a regular polygon is 162 degrees. If the figure has side lengths of 12 cm, calculate the perimeter.

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Question 907255: The Measure of each interior angle of a regular polygon is 162 degrees. If the figure has side lengths of 12 cm, calculate the perimeter.
Answer by solver91311(24713) About Me  (Show Source):
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The sum of measures of the interior angles of any n-gon is given by . Since this is a regular polygon and since the number of interior angles of any polygon is equal to the number of vertices is equal to the number of sides, if the measure of one interior angle is 162 degrees, then the sum of the measures of the interior angles must be , hence:



So solve for to determine the number of sides and multiply the number of sides times the given measure of one side to get the perimeter.

John

My calculator said it, I believe it, that settles it