If the difference between the exterior regular polygon and an (n+1) sided regular polygon is 12 find the value of n.

1 answer

The wording looks jumbled

The exterior angle of an n-gon is 360/n
and the exterior angle of an (n+1)-gon is 360/(n+1)

so 360/n - 360(n+1) = 12
times n(n+1) , the LCD
360(n+1) - 360n = 12n(n+1)
360n + 360 - 360n = 12n^2 + 12n
12n^2 + 12n - 360 = 0
n^2 + n - 30 = 0
(n+6)(n-5) = 0
n = 5 or n = a negative

n = 5

check:
the exterior angle of a regular pentagon is 72°
the exterior angle of a hexagon is 60°
which is a difference of 12°