the angles of a polygonare in a.p with common difference 5.if the smallest angle is 120 ,find the no. of sides of the polygon
Answers
Answered by
25
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
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
Similar questions