SOLUTION: I am a regular polygon with one exterior angle of 20 degrees. What is the sum of my interior angles?

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Question 855787: I am a regular polygon with one exterior angle of 20 degrees. What is the sum of my interior angles?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The measures of the n exterior angles, each measuring 20%5Eo , add up to 360%5Eo , so
n%2A20%5Eo=360%5Eo-->n=360%5Eo%2F20%5Eo-->n=18 .
THe polygon has 18 exterior angles, 18 sides, 18 vertices, 18 interior angles.
Each interior angle is supplementary to the adjacent exterior angle,
so each interior angle measure 180%5Eo-20%5Eo=160%5Eo .
The sum of the measures of the 18 interior angles, each measuring 160%5Eo is
18%2A160%5Eo=highlight%282880%5Eo%29 .