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)