G2.4 In the figure, vertices of equilateral triangle $A B C$ are connected to $D$ in straight line segments with $A B=A D$. If $\angle B D C=\alpha^{\circ}$, determine the value of $\alpha$.
Use $A$ as centre, $A B$ as radius to draw a circle to pass through $B, C, D$.
$$
\begin{array}{l}
\angle B A C=2 \angle B D C\left(\angle \text { at centre twice } \angle \text { at } \odot^{\mathrm{ce}}\right) \\
60^{\circ}=2 \alpha^{\circ} \\
\alpha=30
\end{array}
$$