SOLUTION: In a regular polygon, the ratio of the measure of the exterior angle to the measure of the adjacent interior angle is 1 to 4. How many sides does the polygon have?
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Question 196757: In a regular polygon, the ratio of the measure of the exterior angle to the measure of the adjacent interior angle is 1 to 4. How many sides does the polygon have? Answer by solver91311(24713) (Show Source):
The sum of the interior angles in degrees of any polygon is given by:
where is the number of sides of the polygon.
The sum of the exterior angles of any polygon is 180 degrees.
So if you have a regular n-gon where one of the interior angles is 4 times larger than the adjacent exterior angle, then the sum of the interior angles must be 4 times the sum of the exterior angles, so:
