The interior angles of a polygon are in AP The smallest angle is `120` and the common difference is 5. Find the number of sides of the polygon.

Options

A. One
B. Two
C. Three
D. Infinitely many

Answer

A

Explanation

Here, `a=120^(@)" and "d=5.`
Sum of angles of polygon `=(n-2)180^(@)`
`implies(n)/(2)[2a+(n-1)d]=(n-2)180`
`implies(n)/(2)[2xx120+(n-1)5]=(n-2)180`
`impliesn^(2)-25n+144=0`
`implies(n-9)(n-16)=0`
`:.n=9,16`
For `n=9,T_(9)=120+(9-1)5=160`
For `n=16,T_(16)=120+(16-1)5=195" "["not possible"]`