We know that,
Let the number of sides the given polygon have = n
Now,
The number of line segments obtained by joining n vertices = nC2
So, number of diagonals of the polygon = nC2 – n = 44
n(n - 1)/2 - n = 44
n2 – 3n – 88 = 0
(n – 11) (n + 8) = 0
n = 11 or n = – 8
The polygon has 11 sides.