The number of diagonals in a regular polygon of $n$ sides is given by the following formula ${ }^{n} C_{2}-n$
$\therefore $ The number of diagonals in a regular polygon of 100 sides
$={ }^{100} C_{2}-100=\frac{100 \cdot 99}{2}-100$
$=\frac{9900-200}{2} =\frac{9700}{2}=4850$