An exterior angle of a n-sided regular polygon = \(\frac{360}{n}\) For (n - 1) sided regular polygon = \(\frac{360}{n - 1}\) For (n + 2) sided regular polygon = \(\frac{360}{n + 1}\) ⇒ \(\frac{360}{n - 1} - \frac{360}{n + 2}\) = 6 9Given) ⇒ \(\frac{360(n + 2) - 360(n - 1)}{(n - 1)(n + 2)}\) ⇒ \(\frac{360n + 720 - 360n + 360}{(n - 1)(n + 2)}\) ⇒ \(\frac{1080}{(n - 1)(n + 2)} = \frac{6}{1}\) ⇒ 1080 = 6 (n - 1)(n + 2) ⇒ 180 = (n - 1)(n + 2) ⇒ 180 = n\(^2\)+ 2n - n - 2 ⇒ 180 = n\(^2\) + n - 2 ⇒ n\(^2\)b+ n - 2 - 180 = 0 ⇒ n\(^2\) + n - 182 = 0 ⇒ n\(^2\) + 14n - 13n - 182 = 0 ⇒ n (n + 14) - 13 (n + 14) = 0 ⇒ (n - 13) (n + 14) = 0 ⇒ n - 13 = 0 or n + 14 = 0 ⇒ n = 13 or n = -14 ∴ n = 13 (We can't have a negative number of side)