2. In trapezoid $A B C D$, $A D / / B C, A B=A C$, $B C=B D=(\sqrt{2}+1) C D$. Then the degree measure of $\angle B A C+\angle B D C$ is $\qquad$ .
2.180 .

As shown in Figure 5, draw $A E \perp B C$ at $E$ and $D F \perp B C$ at $F$. Then
$$
\begin{array}{l}
B E=E C=\frac{1}{2} B C, \\
\angle C A E=\frac{1}{2} \angle B A C,
\end{array}
$$

and quadrilateral $A E F D$ is a rectangle.