3. As shown in Figure $2, A A^{\prime} 、 B B^{\prime}$ are the bisectors of $\angle E A B 、 \angle D B C$ respectively. If $A A^{\prime}=B B^{\prime}$
$=A B$, then the degree measure of $\angle B A C$
is $\qquad$ .
3. 12 ${ }^{\circ}$.

Let the degree of $\angle B A C$ be $x$.
Since $A B=B B^{\prime}$, thus $\angle B^{\prime} B D=2 x, \angle C B D=4 x$.
Also, since $A B=A A^{\prime}$, then
$\angle A A^{\prime} B=\angle A B A^{\prime}=\angle C B D=4 x$.
Since $\angle A^{\prime} A B=\frac{1}{2}\left(180^{\circ}-x\right)$,
thus $\frac{1}{2}\left(180^{\circ}-x\right)+4 x+4 x=180^{\circ}$, solving for $x$ gives $x=12^{\circ}$.