Question

The difference between the exterior angles of two regular polygons, having the sides to

(n – 1) and (n + 1) is 9°. Find the value of n.​

Answer 1

${\huge{\underline{\underline{\mathcal{\blue{♡Answer♡}}}}}}$

We know that sum of exterior angles of a polynomial is 360°

(i) If sides of a regular polygon = n – 1

Then each angle = 360°/(n – 1)

And if sides are n + 1, then

Each angle = 360°/(n + 1)

According to the condition,

360°/(n – 1) – 360°/(n + 1) = 9

●●》 360 [1/(x – 1) – 360/(n + 1) = 9

●●》 360 [(n + 1 – n + 1)/(n – 1)(n + 1)]= 9

●●》(2 × 360)/n2 – 1 = 9 ⇒ n2 – 1 = (2 × 360)/9 = 80

●●》n2 – 1 = 80

●●》n2 = 1- 80 = 0

●●》 n2 – 81 = 0

●●》 (n)2 – (9)2 = 0

●●》 (n + 9) (n – 9) = 0

Either n + 9 = 0, then n = -9 which is not possible being negative,

Or n – 9 = 0, then n = 9

∴ n = 9

∴ No. of sides of a regular polygon = 9