Question

The difference between an exterior angle of (n - 1) sided regular polygon and an exterior angle of (n + 2) sided regular polygon is 6° find the value of n.

Answer 1

Exterior angle = `360/ (n - 1)`

Exterior angle = `360/ (n + 2)`

`360/(n-1)-360/(n+2)=6°`

`360[1/(n-1)-1/(n+2)]=6°`

`360[((n+2)-(n-1))/((n-1)(n+2))]=6°`

`60[(n+2-n+1)/(n^2+2n-n-2)]=1`

`60[3/(n^2+n-2)]=1`

180 = n² + n - 2

0 = n² + n - 2 - 180

0 = n² + n - 182

0 = n² + (14 - 13)n - 182

0 = n² + 14n - 13n - 182 

0 = n(n + 14) -13(n - 14)

0 = (n + 14) (n - 13)

n + 14 = 0 or n - 13 = 0

n = -14 or n = 13