Question

In a regular polygon, the ratio of the measure of an exterior angle to the measure of an interior angle is 2:13. How many sides does the polygon have?

Answer 1

Exterior angle + interior angle = 180º
2x + 13x = 180
x = 12
2x = 24

Sum of interior angles = 180º(n-2)
One interior angle = 180º(n-2)/n
180º(n-2)/n = 24
n = 30/13

This polygon shouldn't exist.

Answer 2

the answer in the back of the book is 15 sides :/ so idk...

Answer 3

Oh, I'm sorry, I mixed up the ratio.

x = 12
13x = 156
180(n-2)/n = 156
n = 15