Explanation

(a)
Let number of sides of polygon=$n$
$\Rightarrow \ \ \ \ \ \ {\ ^{n}C}_{2} - n = 44$ [given]
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \frac{n!}{2!(n - 2)!} - n = 44$
$\Rightarrow \ \ \ \ \ \ \ \ \ n(n - 1) - 2n = 88$
$\Rightarrow \ \ \ \ n^{2} - 3n - 88 = 0$
$\Rightarrow \ \ \ \ \ \ (n - 11)(n + 8) = 0\ \ \ \ \ \Rightarrow \ \ \ \ \ \ n = 11,\ - 8$
Since, sides cannot be negative
$\therefore\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ n = 11$