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Solution: A polygon of n sides 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 segments obtained by joining the vertices of a n sided polygon taken two at a time is nC2 = n(n − 1)/ 2 . Out of these lines, there are n sides of polygon. Therefore, number of diagonals of the polygon is n(n − 1)/ 2 − n = n(n − 3)/ 2 . In particular for a pentagon and heptagon (Septagon), number of diagonals respectively are 5(5−3)/ 2 = 5 and 7(7−3)/ 2 = 14.
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