5. A convex quadrilateral $A B C D$ is inscribed in a circle. Its diagonal $B D$ is the bisector of the angle at vertex $B$, forms an acute angle of $65^{\circ}$ with the other diagonal and an angle of $55^{\circ}$ with side $A D$. Find the angles of the quadrilateral.
Answer: $65^{\circ}, 120^{\circ}, 115^{0}, 60^{0}$ or $115^{\circ}, 20^{\circ}, 65^{0}, 160^{0}$.

## Grading Criteria for the Final Round of the Rosatom Olympiad 04.03.2023 8th Grade

In all problems, the correct answer without justification 0