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 $80^{\circ}$ with the other diagonal and an angle of $55^{\circ}$ with side $A D$. Find the angles of the quadrilateral.
Answer: $80^{0}, 90^{0}, 100^{0}, 90^{0}$ or $100^{0}, 50^{0}, 80^{0}, 130^{0}$.

## Variant 3