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?

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) (Show Source): You can put this solution on YOUR website!
an interior and exterior angle pair are supplementary (add to 180�)

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

so the exterior angle is 2k or 40�

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