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The interior angles of a polygon are in A.P. The smallest angle is $120 °$ and the common difference is $5 °$ . Then the number of sides of the polygon is

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Detailed Solution

\frac{n}{2} [2 (120) + (n - 1) 5] = (2 n - 4) 90 °

$n [240 + 5 n - 5] = (2 n - 4) 180$

$240 n + 5 n^{2} - 5 n = 360 n - 720$

$5 n^{2} - 365 n + 240 n + 720 = 0$

$\Rightarrow 5 n^{2} - 125 n + 720 = 0$

$\Rightarrow n^{2} - 25 n + 144 = 0$

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

$\Rightarrow n = 16$ (or) 9.

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