Five, (12 points) As shown in the figure, in isosceles $\triangle ABC$, $AB = AC$, the vertex angle $A = 20^{\circ}$, and a point $D$ is taken on side $AB$ such that $AD = BC$. Find the measure of $\angle BDC$.
Five, Hint: Construct a regular $\triangle A C E$ outside $\triangle A B C$ with $A C$ as a side, and connect $D E$. Then $\triangle A B C \cong \triangle E A D$, so $\triangle E D C$ is an isosceles triangle. It is easy to find that $\angle B D C=30^{\circ}$.