We are given : Number of diagonals of a polygon = 1127 diagonals.
We know relation between number of diagonals and number of sides of the polygon.
Plugging d=1127 in above formula, we get
[tex]\frac{n(n-3)}{2}=1127[/tex]
Multiplying both sides by 2, we get
[tex]n(n-3)=2254[/tex]
[tex]n^2-3n=2254[/tex]
[tex]n^2-3n-2254=0[/tex]
Solving quadratic equation by factoring, we get factors
[tex]\left(n-49\right)\left(n+46\right)=0[/tex]
Solving for n, we get
n-49=0
n=49.
n+46=0.
n=-46.
We can't take number of sides by a negative number.
Therefore, number of sides does the polygon have 49 side.
