SOLUTION: the measure of each interior angle of a regular polygon is 3 times the measure of each exterior angle. How many sides does the polygon have? how to solve?
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Question 346811: the measure of each interior angle of a regular polygon is 3 times the measure of each exterior angle. How many sides does the polygon have? how to solve? Answer by solver91311(16877) (Show Source):
The interior angle and the corresponding exterior angle of any polygon are a linear pair, hence they are supplementary. From the 3 to 1 relationship we can write:
Since this is a regular polygon, all of the exterior angles are congruent. The sum of the exterior angles of any polygon is , hence for a regular polygon the number of sides is given by:
where is the measure of the exterior angle.
Substitute and solve for
John
My calculator said it, I believe it, that settles it
