Correct Answer - Option 1 : 9
Given
The difference between the exterior angles of the two regular polygons, having the sides equal to (n - 1) and (n + 1) is 9°
Concept
Sum of each each exterior angle = (360°/n)
Calculation
⇒ When number of sides of a regular polygon = (n - 1)
⇒ Each exterior angle = (360°/(n - 1))
⇒ When number of sides of a regular polygon = (n + 1)
⇒ Each exterior angle = (360°/(n + 1))
Now,
Difference is
⇒ [(360°/(n - 1)) - (360°/(n + 1))] = 9°
As 360° is common so take it out
⇒ 360° × [(1/(n -1)) - (1/(n + 1))] = 9°
⇒ [(n + 1 - n + 1)/(n2 - 12)] = (9°/360°)
⇒ (2/(n2 - 1)) = (1/40)
⇒ n2 - 1 = 80
⇒ n2 = 81
⇒ n = 9
∴ Number of side is 9