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.

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