Example 2 As shown in Figure 2, in $\triangle A B C$, $A B=A C, \angle A=20^{\circ}, D$ is a point on $A C$, $\angle D B C=50^{\circ}, E$ is a point on $A B$, $\angle E C B=20^{\circ}$. Find the degree measure of $\angle B D E$.
In $\triangle B C D$, it is easy to see that $B C = D C$. In $\triangle B C E$, it is easy to see that $E C = B C$.
$$
\therefore C D = C E = C B \text {, }
$$

Thus, $C$ is the circumcenter of $\triangle B D E$.
$$
\therefore \angle B D E = \frac{1}{2} \angle B C E = 10^{\circ} \text {. }
$$