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

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 $$ \begin{array}{l} ={ }^{100} C_{2}-100=\frac{100 \cdot 99}{2}-100 \\ =\frac{9900-200}{2}=\frac{9700}{2}=4850 \end{array} $$