Question

if the difference between an exterior angle of a regular polygon and n sides and an exterior angle of a regular polygon of (n-1) one side is equal to 5 degree find the value of n

Answer 1

Formula for measurement of exterior angle = 180 - (360/n)

So, by given condition,
180 - (360/n-1) - [180 - (360/n)] = 5
180 - (360/n-1) -180 + (360/n) = 5
360/n - 360/(n-1) = 5
[360 (n-1) - 360n ] ÷ n (n-1) = 5
360n - 360 - 360n = 5n (n- 1)
-360 = 5n^2 - 5n
5n^2 - 5n +360 = 0
n^2 - n + 72 = 0
(n -9)(n+8) = 0
n = 9

Hope it helps. !! ;-)