Question

If a polygon has 1127 diagonals, how many sides does the polygon have? (what’s the equation to solve or & answer)

Answer 1

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.

$\frac{n(n-3)}{2}=d$, Where n is the number of sides of the polygon and d is number of diagonals.

Plugging d=1127 in above formula, we get

$\frac{n(n-3)}{2}=1127$

Multiplying both sides by 2, we get

$n(n-3)=2254$

$n^2-3n=2254$

$n^2-3n-2254=0$

Solving quadratic equation by factoring, we get factors

$\left(n-49\right)\left(n+46\right)=0$

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.