Question

If the interior angles of a polygon are in ap suc hthat the smallest angle is 120 degree and common difference is 5 degree find the number of sides of the polygon

Answer 1

Sum of all angles = (n-2)x180

Sigma (Tn) = (n-2)180

Sigma ( a+(n-1)d) = (n-2)180

Sigma (120 +5n - 5) = (n-2)180

115n + 5 x (n(n+1))/2 = (n-2)180

115n + 2.5 (n2 + n) - 180n + 360 = 0

2.5n2 - 62.5 n + 360 = 0

Answer is n = 9 & 16

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