Question

The number of diagonals in a polygon having ‘n’ number of sides is

Answer 1

Step-by-step explanation:

A Polygon of n sides has n vertices.By joining any two vertices of a polygon,we abtain either a side or a diagonal of the polygon.Number of line segments obtained by joining the vertices of an n sided polygon taken two at a time

=Number of ways of selecting 2 out of n=

nc2=n(n-1)/2

Out of these lines,n lines are the sides of the polygon.

Therefore,Number of diagonals of the

polygon=n(n-1)/2-n=n(n-3)/2