Question

A convex polygon has $44$ diagonals , find no of sides.

Answer 1

Let the number of sides of the polygon = n

Therefore, number of angular points = n

Number of straight lines joining any two of these n points = $n_{C_2}$

Number of diagonals = $n_{C_2}-n$

$n_{C_2}-n$ = $44$

$\frac{n(n-1)}{2}-n=44$

$n^2-3n-88=0$

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

$n=11$

Hence, the number of sides is 11.