G4.1 In Figure $1, A E$ and $A D$ are two straight lines and $A B=B C=C D=D E=E F=F G=G A$.
If $\angle D A E=\alpha^{\circ}$, find the value of $\alpha$.
$\begin{array}{l}\angle A F G=\alpha^{\circ}=\angle A C B \text { (base } \angle \text { s isos. } \triangle \text { ) } \\ \angle C B D=2 \alpha^{\circ}=\angle F G E(\text { ext. } \angle \text { of } \triangle \text { ) } \\ \angle F E G=2 \alpha^{\circ}=\angle B D C(\text { base } \angle \mathrm{s} \text { isos. } \triangle) \\ \angle D F E=3 \alpha^{\circ}=\angle D C E(\text { ext. } \angle \text { of } \triangle \text { ) } \\ \angle A D E=3 \alpha^{\circ}=\angle A E D(\text { base } \angle \text { s isos. } \triangle) \\ \alpha^{\circ}+3 \alpha^{\circ}+3 \alpha^{\circ}=180^{\circ}(\angle \mathrm{s} \text { sum of } \triangle) \\ \alpha=\frac{180}{7}\end{array}$