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
9
Each exterior angle of an (n - 1) sided regular polygon
=360∘n−1
Each exterior angle of an (n + 1) sided regular polygon
=360∘n+1
Given:
360∘n−1−360∘n+1=9∘
⇒360°(1n−1−1n+1)=9∘
⇒40(n+1−(n−1)(n−1)(n+1))=1
⇒40(n+1−n+1)=n2−1
⇒80=n2−1
⇒n2=81
⇒n=9 or −9
As number of sides is positive, n = 9