I4.2 If a regular $Q$-sided polygon has $P$ diagonals, find the value of $Q$
The number of diagonals $={ }_{Q} C_{2}-Q=35$
$$
\begin{array}{l}
\frac{Q(Q-1)}{2}-Q=35 \\
Q^{2}-3 Q-70=0 \\
Q=10
\end{array}
$$