Example 2 Given in $\triangle A B C$, $A B=A C$, $\angle A=20^{\circ}, D 、 E$ are points on $A C 、 A B$ respectively, $\angle D B C=60^{\circ}, \angle E C B=50^{\circ}$. Find the degree measure of $\angle B D E$.
Solution: As shown in Figure 5, let $E^{\prime}$ be the symmetric point of $E$ with respect to $AC$. Connect $E^{\prime}A$, $E^{\prime}B$, $E^{\prime}C$, $E^{\prime}D$, and $E^{\prime}E$. It is known that $\triangle E^{\prime}EC$ is an equilateral triangle, $BE^{\prime}$ is the perpendicular bisector of $EC$, and $D$ is the incenter of $\triangle ABE^{\prime}$. Therefore,
$$
\angle AE^{\prime}D = \frac{1}{2} \angle AE^{\prime}B =
$$
$50^{\circ}$, which gives $\angle AED = 50^{\circ}$.
$$
\therefore \angle BDE = \angle AED - \angle ABD = 30^{\circ}.
$$

This problem utilizes the construction of an equilateral triangle, which can be proven in multiple ways (limited by space, not detailed).

From the above two examples, we can see the importance of constructing equilateral triangles in solving problems. In what situations should we think of constructing an equilateral triangle?