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  4. If a convex polygon has 44 diagonals, then the number of its sides is

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Q. If a convex polygon has $44$ diagonals, then the number of its sides is

Solution:

$n_{c_{2}}-n=44 $
$\Rightarrow \frac{n(n-1)}{2}-n=44$
$n^{2}-3 n-88=0$,
$ n=11,-8$
$ \Rightarrow n=11$