Question

Interior angle of polygon are in A.P.If the smallest angle is `120^@` and the common difference is `5^@`, find the number of sides of polygon.

Answer 1

Sum of interior angles of a `n`-sided polygon is `(n-2)**180`.
Now, we are given, angles are in AP such that ,
`a = 120 and d = 5`
`:. n/2(2a+(n-1)d) = (n-2)180`
`=> n/2(240+(n-1)5) = 180n-360`
`=>n(235+5n) = 360n-720`
`=>5n^2+235n-360n+720 = 0`
`=>5n^2-125n+720 = 0`
`=>n^2-25n+144 = 0`
`=>n^2-16n-9n+144 = 0`
`=>n(n-16)-9(n-16) = 0`
`=>(n-16)(n-9) = 0`
`n=16 and n = 9`
So, number of sides in the given polygon can be `16` or `9`.