21. In the convex quadrilateral $A B C D$, angle $A B D$ is $65^{\circ}$, angle $C B D$ is $35^{\circ}$, angle $A D C$ is $130^{\circ}$, and $A B=B C$. Find the angles of the quadrilateral $A B C D$.
85.21. Answer. $\angle D A B=57^{\circ} 30^{\prime}, \quad \angle A B C=100^{\circ}, \angle B C D=$ $=72^{\circ} 30^{\prime}$. Use the fact that points $A, C$ and $D$ lie on a circle with center $B$.