a polygon of 16 sides

We have given that polygon has 16 vertices and each side and diagonal can be formed by joining two vertices of a polygon,

Let us assume the no. of diagonals of the polygon are N,

⇒ N = (no. of lines formed on joining any two vertices) – (no. of sides of the polygon)

⇒ N = ¹⁶C₂ – 16

We know that ,

And also n! = (n)(n – 1)......2.1

⇒

⇒

⇒

⇒ N = 120 – 16

⇒ N = 104

∴ The total no. of diagonals formed are 104.