G3.2 In Figure $1, A D, D G, G B, B C, C E, E F$ and $F A$ are line segments. If $\angle F A D+\angle G B C+\angle B C E+\angle A D G+\angle C E F+\angle A F E+$ $\angle D G B=r^{\circ}$, find the value of $r$.
In the figure, let $P, Q, R, S, T$ be as shown.
$$
\begin{array}{l}
\angle A T P+\angle B P Q+\angle D Q R+\angle E R S+\angle G S T=360^{\circ} \ldots \ldots \text { (1) } \\
\angle A P T+\angle C Q P+\angle D R Q+\angle F S R+\angle G T S=360^{\circ} \ldots \ldots \text { (2) } \\
\text { (sum of ext. } \angle \text { of polygon) } \\
\angle F A D=180^{\circ}-(\angle A T P+\angle A P T)(\angle \mathrm{s} \text { sum of } \triangle \text { ) } \\
\angle G B C+\angle B C E=360^{\circ}-(\angle B P Q+\angle C Q P)(\angle \mathrm{s} \text { sum of polygon) } \\
\angle A D G=180^{\circ}-(\angle D Q R+\angle D R Q)(\angle \mathrm{s} \text { sum of } \triangle) \\
\angle C E F+\angle A F E=360^{\circ}-(\angle E R S+\angle F S R)(\angle \mathrm{s} \text { sum of polygon) } \\
\angle D G B=180^{\circ}-(\angle G S T+\angle G S T)(\angle \text { s sum of } \triangle)
\end{array}
$$

Add these 5 equations up and make use of equations (1) and (2):
$$
r^{\circ}=180^{\circ} \times 7-2 \times 360^{\circ} \Rightarrow r=540
$$

Remark: The original question $\angle F A D+\angle G B C+\angle B C E+\angle A D G+\angle C E F+\angle D G B=r^{\circ}$ $\angle A F E$ is missing, the original question is wrong.
中文版題目：“...及及 $F A$ 都是綫段。...” is changed into “...及及 $F A$ 都是直䋐綫段。...”