SOLUTION: The measure of each exterior angle of a regular polygon is 2/13 of the measure of each interior angles. Find the number of sides and diagonals of the polygon.

Question 634652: The measure of each exterior angle of a regular polygon is 2/13 of the measure of each interior angles. Find the number of sides and diagonals of the polygon.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The measure of each exterior angle of a regular polygon is 2/13 of the measure of each interior angles. Find the number of sides and diagonals of the polygon.
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I = Interior angle
E = exterior angle = 2I/13
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E + I = 180
I + 2I/13 = 180
15I/13 = 180
I/13 = 12
I = 156 degs
E = 180 - I = 24 degs
number of sides = 360/24 = 15

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