find the interior angle of a polygon is in A.P the smallest angle is 120° the common difference 5° . find the number of sides of polygon?
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Smallest angle=120degree
Common difference=5
A P is 120, 125, 130,……..
The sum of interior angles of a polygon= (n-2)180
Hence Sum of n terms of an A P = (n-2)180
n/2 {2.120+(n-1)5} = 180(n-2)
5n^2 -125n +720 = 0
n^2 -25n +144=0
n=9 or 16
hence number of sides can be 9 or 16
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