A polygon has 44 diagonals the number of its sides is?

Let there be n sides of the polygon. Then it has n vertices.
The total number of straight lines obtained by joining n vertices by talking 2 at a time is ⁿC₂
These ⁿC₂ lines also include n sides of polygon.
Therefore, the number of diagonals formed is ⁿC₂ - n.
Thus, ⁿC₂ - n = 44
⇒ [n(n - 1)/2] - n = 44
⇒ ( n² - 3n) / 2 = 44
⇒ n² - 3n = 88
⇒ n² - 3n - 88 = 0
⇒(n - 11) (n + 8) = 0
∴ n = 11