Question

. If the difference between the exterior angle of a ‘n’ sided regular polygon and an (n+1)

sided regular polygon is 120 , find the value of ‘n’.​

Answer 1

Answer:

Hope this helps you

Step-by-step explanation:

When number of sides of a regular polygon = n, 

The value of its each exterior angle = n360∘

When number of sides of a regular polygon = n+1,

The value of its each exterior angle = n+1360∘

Given n360∘−n+1360∘=12∘

 

⇒360∘(n+1)−360∘(n)=12∘(n+1)n

⇒360∘[n+1−n]=12∘(n2+n)

⇒360∘=12∘(n2+n)

⇒30∘=n2+n

⇒n2+n−30=0

⇒(n+6)(n−5)=0

⇒n=5 or  n=−6

Since, n can't  be negative.

∴n=5