Example 2 As shown in Figure 1,
$$
\begin{array}{l}
\angle A+\angle B+\angle C+ \\
\angle D+\angle E+\angle F+ \\
\angle G=(\quad)
\end{array}
$$
(A) $360^{\circ}$
(B) $450^{\circ}$
(C) $540^{\circ}$
(D) $720^{\circ}$
$$
\begin{array}{l}
\angle B+\angle B M N+\angle E+\angle G=360^{\circ}, \\
\angle F N M+\angle F+\angle A+\angle C=360^{\circ} . \\
\text { Also } \angle B M N+\angle F N M=\angle D+180^{\circ} \text {, then } \\
\angle A+\angle B+\angle C+\angle D+\angle E+\angle F+\angle G \\
=540^{\circ} .
\end{array}
$$