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Question
Write the number of diagonals of an n-sided polygon.
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Solution
An n-sided polygon has n vertices.
By joining any two vertices of the polygon, we obtain either a side or a diagonal of the polygon.
Number of line segments obtained by joining the vertices of an n-sided polygon if we take two vertices at a time = Number of ways of selecting 2 out of n = nC2
Out of these lines, n lines are sides of the polygon.
Number of diagonals of the polygon = \[{}^n C_2 - n = \frac{n (n - 1)}{2} - n = \frac{n(n - 3)}{2}\]
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