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From n vertices of a polygon, the total number of line segments that can be drawn by joining any two vertices is given by nC2.nC2 = n(n-1) / 2.These line segments include both the sides of the polygon and its diagonals.An n-sided polygon has n sides.To find the number of diagonals, we subtract the number of sides from the total number of line segments:Number of diagonals = nC2 - n= [n(n-1) / 2] - n= [n(n-1) - 2n] / 2= [n^2 - n - 2n] / 2= [n^2 - 3n] / 2= n(n-3) / 2.