Question

Q.1

Answer 1

Let the number of sides of a polygon be n. 

The smallest angle `= 120°=a`

Common difference in angles`=d=5°`

Now, in a polygon of n sides, the sum of interior angles`=(2n-4)xx90°`

`⇒ n/2[2xx120°+(n-1)xx5°]=(2n-4)xx90°`

`⇒n/2[240°+5n-5°]=180n-360°`

`⇒n[235°+5n]=360n-720°`

`⇒235n+5n^2=360n-720`

`⇒5n^2-125n+720=0`

`⇒n^2-25n+144=0`

`⇒n^2-16n-9n+144=0`

`⇒n(n-16)9n+144=0`

`⇒(n-16)(n-9)=0`

`⇒n=16 or n=9`