The interior angles of a convex polygon are in arithmetic progression. The smallest angle is 120 degrees and the common difference is \(5\) degrees. Find the number of sides of the polygon.

Guest Jan 13, 2022

#2**+1 **

I got a different answer from Cphill...

We know sum of all the interior angles of a polygon having n sides = (n-2)180

Given smallest angle = 120

a = 120

d = 5

Sum, S = (n/2)(2a+(n-1)d)

(n/2)(240+(n-1)5) = (n-2)180

n(240+5n-5) = (n-2)360

5n2+235n-360n+720 = 0

5n2-125n+720 = 0

n2-25n+144 = 0

(n-9)(n-16) = 0

n = 9 or 16.

n = 16 cannot be possible since interior angle cannot be greater than 180.

XxmathguyxX Jan 13, 2022