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The interior angles of a polygon are in ...

The interior angles of a polygon are in A.P .The smallest angle is `120^(@)` and common difference is `5^(@)` . Find the number of the polygon.

Text Solution

Verified by Experts

`a=120,d=5,n=`?
`S_(n)=(2n-4)90=(n-2)180`.
Also `S_(n)=(n)/(2)[2(120)+(n-1)5]=(n)/(2)[235+5n]`
`therefore(n-2)180=(n)/(2)(235+5n)`
`(n-2)360=n(235+5n)`.
`360n-720=235n+5n^(2)`
`5n^(2)-125n+720=0`
`5n^(2)-80n-45n+720=0`
`5n(n-16)-45(n-16)=0` `(n-16)(5n-45)=0rArrn=16,9`
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