A polygon has $20$ diagonals then the number of its sides are:

5

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8

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7

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11

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Solution

The correct option is B $8$
Number of diagonals $=^{n} C_{2} - n$
$\Rightarrow \frac{1}{2} n (n - 1) - n = 20 \Rightarrow n^{2} - 3 n - 40 = 0 \Rightarrow (n + 5) (n - 8) = 0 n = - 5, 8$
Negative value is neglected so $n = 8$

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