Question

A polygon has $90$ diagonals. Find the number of its sides?

Answer 1

Number of diagonals of a polygon$=\frac{n(n-3)}{2}$

$\frac{n(n-3)}{2}=90$

$n(n-3)=180$

$n^2-3n-180=0$

$n^2-15n+12n-180=0$

$(n-15)(n+12)=0$

$n\ne -12$

$\therefore n=15$

$\therefore$ The polygon has $15$ sides.