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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.
Solution
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
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