An exterior angle of a n-sided regular polygon =
For (n - 1) sided regular polygon =
For (n + 2) sided regular polygon =
⇒ − = 6 9Given)
⇒ | 360(n+2)−360(n−1) |
| (n−1)(n+2) |
⇒ | 360n+720−360n+360 |
| (n−1)(n+2) |
⇒ =
⇒ 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)