Question

There are two regular polygons with number of sides equal to (n 1) and (n + 2). Their exterior angles differ by 6. The value of n

Answer 1

Step-by-step explanation:

360°

-

360°

= 6°

(n - 1) (n + 2)

⇒ 360°

n + 2 - n + 1

= 6°

(n - 1)(n + 2)

⇒ (n – 1) (n + 2) = 180°

n² + n – 2 = 180

n² + n – 182° = 0

n² + 14n – 13n – 182 = 0

n(n + 14) – 13 (n + 14) = 0

(n + 14) (n – 13) = 0

n = 13, – 14 [ ∴ n ≠ –14]