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Question

If the difference between an exterior angle of an (n - 1) sided regular polygon and an (n + 1) sided regular polygon is 9, the value of ‘n’ is


A

9

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B

8

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C

10

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D

6

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Solution

The correct option is A

9


Each exterior angle of an (n - 1) sided regular polygon

=360n1

Each exterior angle of an (n + 1) sided regular polygon

=360n+1

Given:
360n1360n+1=9

360°(1n11n+1)=9
40(n+1(n1)(n1)(n+1))=1
40(n+1n+1)=n21
80=n21
n2=81
n=9 or 9
As number of sides is positive, n = 9


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