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A polygon has 44 diagonals, then the number of its sides are ?

13
9
11
7

Correct Answer: 11

Explanation:

Let the number of sides be n.

The number of diagonals is given by ⁿC₂ - n

^{Therefore, n}C₂ - n = 44, n>0

ⁿC₂ - n = 44

n²- 3n - 88 = 0

n²-11n + 8n - 88 = 0

n(n - 11) + 8(n - 11) = 0

n = -8 or n = 11.

As n>0, n will not be -8. Therefore, n=11.

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