## Task A-2.5.

Given is a trapezoid $A B C D$ with bases $\overline{A B}$ and $\overline{C D}$, such that triangle $A B C$ is acute-angled. Let $O$ be the center of the circumcircle of triangle $A B C$, and point $E$ the intersection of lines $O B$ and $C D$. If $\varangle D B C=\varangle C E B+10^{\circ}$, determine the measure of the angle between the diagonals of trapezoid $A B C D$.
Scoring: It is possible to have correct solutions that logically arrive at the answer $100^{\circ}$, for example, by considering the angle $\varangle A S B$. Although the angle between two lines is defined as the smaller of the two possible angles, such solutions (if the reasoning is complete) should be scored with all 6 points.

3 points are awarded for recognizing the relationship between the angles $\varangle A C B$ and $\varangle A O B$ as central and inscribed angles over the chord $A B$. Noting that the angles $\varangle C E B$ and $\varangle O B A$ are congruent earns 1 point. Expressing the angle $\varangle A O B$ in terms of $\alpha$ earns 1 point, even if the solution is not complete and does not mention the central and inscribed angles. The correct final result earns 1 point.