## Task B-1.2.

If the number of sides of a regular polygon is increased by 4, the number of diagonals increases by 94. Determine the number of diagonals of the polygon before the increase in the number of sides.
## Solution.

Let $n$ be the number of sides of the polygon, and $d$ be the number of its diagonals. The formula for calculating the number of diagonals of a regular polygon is $d=\frac{n(n-3)}{2}$.

According to the condition of the problem, we get the equation:

$$
\frac{n(n-3)}{2}+94=\frac{(n+4)(n+1)}{2}
$$

After rearranging, we have in sequence:

$$
\begin{aligned}
n(n-3)+188 & =(n+4)(n+1) \\
n^{2}-3 n+188 & =n^{2}+5 n+4 \\
8 n & =184
\end{aligned}
$$

It follows that $n=23$.

The total number of diagonals is $d=\frac{23 \cdot(23-3)}{2}=230$.