Question

if the difference between the exterior angle of a n sided polygon and n-1 sided polygon is 12, Find the value of n​

Answer 1

Exterior angle = 360/n

So 360/n- 360/n-1=12

360( n-1)- 360n/n^2-n=12

12n^2-12n= 360

12n^2-12n-360= 0

n^2 -n-30=0

n^2-6n+5n-30=0

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

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

n = 6 or -5

but n can't be negative so n = 5

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