If the difference between an exterior angle of a regular polygon of n sides and exterior angle of another regular polygon of (n + 1) sides is equal to 30°. Then the value of n is:

Each exterior angle of a regular polygon of n sides = 360˚ /n Each exterior angle of a regular polygon of (n+1) sides = 360˚ /(n+1) Difference between the two exterior angles = 30˚ According to the question, => (360˚ /n) – [360˚ /(n+1)] = 30˚ => (12/n) – [12/(n+1)] = 1 => (12n + 12 – 12n)/[n(n+1)] = 1 => 12 = n² + n => n² + n – 12 = 0 => n² + 4n – 3n – 12 = 0 => n(n + 4) – 3(n + 4) = 0 => (n + 4) (n - 3) = 0 => n = -4 or n = 3 Therefore value of n is 3 (as value of n cannot be in negative).