Question

If the difference between the exterior angle of a n sided regular polygon and an (n 1) sided regular polygon is 12. find the value of n.

Answer 1

Sum of exterior angle of a polygon is 360°
An n-sided polygon has n equal exterior angles.

360/n - 360/(n + 1) = 12
360(n + 1) - 360n = 12n(n + 1)
12n^2 + 12n = 360
n^2 + n - 30 = 0
(n - 5)(n + 6) = 0
n = 5 or n = -6

Therefore, n = 5