1. Four points $A, B, C, D$ in the same plane satisfy
$$
A D=B D=C D, \angle A D C=160^{\circ} \text {. }
$$

Then the degree of $\angle A B C$ is
2. $80^{\circ}$ or $100^{\circ}$.
From the given information, point $D$ is the center of the circumcircle of $\triangle A B C$.
If point $B$ is on the major arc $\overparen{A C}$, then
$$
\angle A B C=\frac{1}{2} \angle A D C=80^{\circ} \text {; }
$$

If point $B$ is on the minor arc $\overparen{A C}$, then
$$
\angle A B C=180^{\circ}-\frac{1}{2} \angle A D C=100^{\circ} \text {. }
$$