Problem 2. Pentagon $A B C D E$ is inscribed in circle $\omega$. Diagonal $A C$ is the diameter of circle $\omega$. Find $\angle B E C$, if $\angle A D B=20^{\circ}$.
Answer: $70^{\circ}$.

Solution. Fig. 4. Since $\angle A D B=20^{\circ}$, the arc $A B$ is $40^{\circ}$. Since $A C$ is a diameter, the arc $A B C$ is $180^{\circ}$, so the arc $B C$ is $180^{\circ}-40^{\circ}=140^{\circ}$. The angle $B E C$ subtends the arc $B C$, which means it is equal to $140^{\circ} / 2=70^{\circ}$.

## Criteria

4 p. Correct solution.

0 p. Only the correct answer.

![](https://cdn.mathpix.com/cropped/2024_05_06_bb219abe882ecbba3775g-2.jpg?height=450&width=497&top_left_y=84&top_left_x=478)

Fig. $4:$ to problem 2