# Self Doubt

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A polygon has 12 edges , How many diagonals does it have?

How to find the number of diagonals?

For any $n$ side polygon, the number of diagonals are $\frac{n(n-3)}{2}$.

We can prove this as follows:

First, select a vertex from the polygon. This can be done in $n \choose 1$ ways.
To draw diagonals, we can choose any other vertex except the neighbouring vertices, giving us $n -1\choose 1$ ways.

This gives us a total of $n \times (n-3)$ diagonals.

However, we have overcounted by a factor of two here, since diagonal from $AB$ is same as diagonal from $BA$.

Hence, the total number of diagonals are $\frac{n(n-3)}{2}$

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