The difference between an exterior angle of (n - 1) sided regular polygon and an exterior angle of (n + 2) sided regular polygon is 6 $^o$ , then the value of "n" is

Correct answer is B

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)

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The difference between an exterior angle of (n - 1) sided regular polygon and an exterior angle of (n + 2) sided regular polygon is 6o^o, then the value of "n" is