Question 966906
the exterior angle of a regular polygon is equal to 360 / n, where nis the number of sides.


the interior angle of a regular polygon is equal to 180 - 360 / n, where n is the number of sides.


the ratio of the interior angle of the polygon to the exterior angle of the polygon is equual to 5/2.


thie means that (180 - 360 / n) / (360 / n) is equal to 5 / 2.


take the cross product to get:


5 * (360 / n) is equal to 2 * (180 - 360 / n)


solve for n to get n = 7.


when n = 7, the exereior angle is 360 / 7 = 51.42857143 degrees.


when n = 7, the interior angle is 180 - 51.42857143 degrees which is equal to 128.5714286 degrees.


the ratio of the interior angle to the exterior angle is equal to 128.5714286 / 51.42857143 which is equal to 2.5.


Multiply the numerator and denominator of 2.5 / 1 to get 5 / 2.


the solution is confirmed as good.


another calculation for the interioa angle would be (n-2) * 180 / n.


when n = 7, that becomes 5 * 180 / 7 which becomes 128.5714286.


the interior angle can be calculated in both ways.


it's the same either way.