SOLUTION: What is the name of an equiangular polygon if the ratio of the measure of an interior angle to the measure of an exterior angle is 7:2? How do I get the answer?

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Question 393430: What is the name of an equiangular polygon if the ratio of the measure of an interior angle to the measure of an exterior angle is 7:2?
How do I get the answer?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
an interior and exterior angle pair are supplementary (add to 180º)

using k as a proportionality constant (fudge factor) ___ 7k + 2k = 180º ___ 9k = 180º ___ k = 20º

so the exterior angle is 2k or 40º

the sum of the exterior angles is 360º ___ 360º / 40º = 9
9 angles AND 9 sides (a nonagon)