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Question
Find the number of diagonals of (ii) a polygon of 16 sides.
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Solution
A polygon of n sides has n vertices. By joining any two vertices we obtain either a side or a diagonal.
∴ Number of ways of selecting 2 out of 9 \[=^n C_2 = \frac{n\left( n - 1 \right)}{2}\]
Out of these lines, n lines are the sides of the polygon.
∴ Number of diagonals =\[\frac{n\left( n - 1 \right)}{2} - n = \frac{n\left( n - 3 \right)}{2}\]
There are 16 sides.
∴ Number of diagonals =\[\frac{16\left( 16 - 3 \right)}{2} = 104\]
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