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The difference between an exterior angle of (n - 1) sided re...

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

A.

11

B.

13

C.

12

D.

14

Correct answer is B

An exterior angle of a n-sided regular polygon = 360n

For (n - 1) sided regular polygon = 360n1

For (n + 2) sided regular polygon = 360n+1

360n1360n+2 = 6 9Given)

360(n+2)360(n1)(n1)(n+2)

360n+720360n+360(n1)(n+2)

1080(n1)(n+2)=61

⇒ 1080 = 6 (n - 1)(n + 2)

⇒ 180 = (n - 1)(n + 2)

⇒ 180 = n2+ 2n - n - 2

⇒ 180 = n2 + n - 2

⇒ n2b+ n - 2 - 180 = 0

⇒ n2 + n - 182 = 0

⇒ n2 + 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)