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Find the number of sides:

+2 votes
asked Aug 19, 2016 in Mathematics by Rahul Roy (7,955 points)
The interior angles of a polygon are in AP the smallest angle is 120 degrees and the common difference is 5 degrees. Find the number of sides of the polygon.

1 Answer

+1 vote
answered Aug 19, 2016 by संजीव कुमार (3,822 points)
selected Aug 19, 2016 by Rahul Roy
Best answer
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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