## Task B-2.2.

Calculate the interior angle of a regular polygon if the total number of all sides and diagonals is 105.
## Solution.

Let the number of sides of the polygon be $n$. Then we have:

$$
n+\frac{n \cdot(n-3)}{2}=105
$$

The positive solution to this quadratic equation is 15.

The internal angle can be calculated using the formula

$$
\begin{aligned}
& \alpha=\frac{(n-2) \cdot 180^{\circ}}{n} \\
& \alpha=156^{\circ}
\end{aligned}
$$