Question

the difference between an exterior angle of a regilar polygon of n sides and an exterior angle of a regilar polygon (n+1) sides is equal to 18 °. Find the number of sides of each polygon. ​

Answer 1

Sum of exterior angle of a polygon is 360°

An n-sided polygon has n equal exterior angles.

360/n - 360/(n + 1) = 12

360(n + 1) - 360n = 12n(n + 1)

12n^2 + 12n = 360

n^2 + n - 30 = 0

(n - 5)(n + 6) = 0

n = 5 or n = -6

Therefore, n = 5

Hope this helps!