11. In $\triangle A B C$, $\angle B A C=30^{\circ}, \angle A B C=70^{\circ}, M$ is a point inside the triangle, $\angle M A B=\angle M C A=20^{\circ}$, find the degree measure of $\angle M B A$.
(Mathematics Teaching Problem 491)
11. Let $\angle M B A=x$, then $\angle M A C=70^{\circ}$. From $\frac{\sin 20^{\circ}}{\sin 60^{\circ}} \cdot \frac{\sin 20^{\circ}}{\sin 10^{\circ}} \cdot \frac{\sin \left(70^{\circ}-x\right)}{\sin x}=1$, and $\sin 60^{\circ} \cdot \sin x=\frac{4 \sin 20^{\circ} \cdot \sin 40^{\circ} \cdot \sin 80^{\circ} \cdot \sin \left(70^{\circ}-x\right)}{2 \sin 40^{\circ}}=\frac{\sin 60^{\circ} \cdot \sin \left(70^{\circ}-x\right)}{2 \sin 40^{\circ}}$, we find that $x=30^{\circ}$.