How many diagonals are there in a polygon with n sides ?

1.	How many diagonals are there in a polygon with n sides ?
Answer» Solution= A polygon of n side has n vertices. By joining any two vertices of a polygon, we obtain either a side or a diagonal of the polygon. Number of line segment obtained by joining the vertices of an n sided polygon taken two at a time= Number of ways of selecting 2out of n =nC2=n(n-1)/2Out of these lines n lines are the sides of the polygon. Number of diagonals of the polygon =n(n-1)/2-n= n(n-3)/2

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