Question

A polygon has 77 diagonals.determine the number of sides?

Answer 1

If a polygon has 77 diagonals it will have 14 number of sides

Answer 2

Answer:

The number so sides of the polygon is 14.

Step-by-step explanation:

Given : A polygon has 77 diagonals.

To determine : The number of sides?

Solution :

The number of diagonals being $d=\frac{n(n-3)}{2}$

where, n is the number of sides.

$77=\frac{n(n-3)}{2}$

$154=n(n-3)$

$n^2-3n-154=0$

$n^2-3n-154=0$

$n^2-14n+11n-154=0$

$n(n-14)+11(n-14)=0$

$(n-14)(n+11)=0$

$n=-11,14$

Reject n=-11 and Accept n=14

Therefore, The number so sides of the polygon is 14.