Question

the difference between an exterior angle of a regular polygon of 'n' sides and an exterior angle of another regular polygon of '(n+1)' sides is equal to 5° ; find the value of 'n'

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Answer 1

Answer:

sum of exterior angle of polygon is 360

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,n=-6

n=5

Answer 2

Answer:

Extr angle= 360/n

360/n-360/n+1 = 5

multiply by n(n+1)

(n+1) 360-360n=5n(n+1)

360n+360-360n=5n2+5n

5 n2+5n-360= 0

n2+n-72=0

n2+9n-8n-72=0

n(n+9)-8(n +9)=0

(n+9), (n-8)

n-8=0

n=8. Ans