The interior angles of a polygon are in A.P. if the smallest angle be 120 degree and the common difference be 5 degree then the number of sides of the polygon is?

Asked by aliencpr31 | 24th Jul, 2019, 10:16: AM

Expert Answer:

Smallest angle = 120°

Common difference = d = 5

A.P. is 120, 125, 130,……..

The sum of interior angles of a polygon = 180(n - 2)

Hence Sum of n terms of an A.P. = 180(n - 2)

n/2 {2 × 120+(n - 1)5} = 180(n-2)

5n2 - 125n + 720 = 0

n2 - 25n + 144 = 0

n = 9 or 16

hence number of sides can be 9 or 16.

Hence, the correct option is c.

Answered by Sneha shidid | 24th Jul, 2019, 10:27: AM

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