Example 1. (1986 Jilin Province Eight Cities Junior High School Mathematics Competition Question) In Figure 1, the degree of $\angle A+\angle B+\angle C+\angle D$ $+\angle E+\angle F$ is $\qquad$ .
Solve $\begin{aligned} & \angle A+(\angle B+\angle C)+(\angle D+\angle E \\ & +\angle F) \\ = & \angle A+\left(180^{\circ}-\angle B P C\right)+\left(360^{\circ}\right. \\ & -\angle F L D) \\ = & {\left[\angle A+\left(180^{\circ}-\angle B P C\right)\right.} \\ & \left.+\left(180^{\circ}-\angle F L D\right)\right]+180^{\circ} \\ = & (\angle A+\angle A P L+\angle A L P)+180^{\circ} \\ = & 180^{\circ}+180^{\circ}=360^{\circ} .\end{aligned}$