The result of dividing the interior angles of a regular polygon by its exterior angle is 2.5, find the number of sides of the polygon
Let the measure of one interior angle = x
And its exterior angle = 180 - x
So
x / ( 180 - x) = 2.5
x = 2.5 (180 - x)
x = 450 - 2.5x
x + 2.5x = 450
3.5x = 450
x = 450 / 3.5 = the measure of an exterior angle
The number of sides is given by
(N - 2) (180) / N = 450/ 3.5 simplify
180N - 360 = (450 / 3.5) N
180N - (450/3.5) N = 360
(630 - 450) N = 360 * 3.5
180N = 1260
N = 1260 / 180 = 7 = the number of sides