The number of diagonals in a regular polygon of $100$ sides is

4950

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4850

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4750

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4650

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Solution

The correct option is B $4850$
The number of diagonals in a regular polygon of $n$ sides is given by the following formula $^{n} C_{2} - n$
$∴$ The number of diagonals in a regular polygon of $100$ sides
$=^{100} C_{2} - 100 = \frac{100.99}{2} - 100$

$= \frac{9900 - 200}{2} = \frac{9700}{2} = 4850$

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