8. As shown in Figure 3, in quadrilateral $A B C D$, $A D / / B C, A B=A C$, a perpendicular line is drawn from point $D$ to $B C$, with the foot of the perpendicular being $F, D F$ intersects $A C$ at point $E$. If $B E=2 D F$, and $B E$ bisects $\angle A B C$, then $\angle B A D=$ $\qquad$ . (China)
8. $144^{\circ}$.

Draw $A M \perp B C$ at point $M$, and draw a perpendicular line to $B C$ through point $B$, intersecting the extension of $C A$ at point $G$.
Thus, $A$ is the circumcenter of Rt $\triangle B C G$
$\Rightarrow A$ is the midpoint of $C G$
$\Rightarrow M$ is the midpoint of $B C$
$$
\begin{array}{l}
\Rightarrow B G=2 A M=2 D F=B E \\
\Rightarrow \angle B G E=\angle B E G=3 \angle A B E \\
\Rightarrow 5 \angle A B E=90^{\circ} \\
\Rightarrow \angle A B E=18^{\circ} .
\end{array}
$$

Therefore, $\angle B A D=90^{\circ}+3 \times 18^{\circ}=144^{\circ}$.