10. In $\triangle A B C$, $A B=A C, \angle A=80^{\circ}, D$ is a point inside the triangle, and $\angle D A B=\angle D B A=10^{\circ}$, find the degree measure of $\angle A C D$.
(Problem 432 from "Mathematics Teaching")
10. Let $\angle A C D=x$, then $\angle B C D=50^{\circ}-x$, from $\frac{\sin 10^{\circ}}{\sin 70^{\circ}} \cdot \frac{\sin 40^{\circ}}{\sin 10^{\circ}} \cdot \frac{\sin x}{\sin \left(50^{\circ}-x\right)}=1$, we find that $x=30^{\circ}$.