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If the ratio of the number of sides of a polygon to the number of diagonals is $2 : 5$ , then the sum of the angles of the polygon is

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$900 °$

$1080^{o}$

$1260^{o}$

$1440^{o}$

answer is B.

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Detailed Solution

$n : \frac{n (n - 3)}{2} = 2 : 5$

$\frac{2 n (n - 3)}{2} = 5 n$

$n (n - 3) = 5 n$

$\begin{array}{l} n^{2} - 3 n - 5 n = 0 \\ n^{2} = 8 n \\ n = 8 \end{array}$

$∴$ Sum of interior angles of polygon $= (n - 2) 180 °$

$= (8 - 2) 180 ° = 6 \times 180 ° = 1080 °$

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