
In this example, a line comes to a corner of "1". 


Let's think about how a line extends in this case.
Arrows mean one of them will have a line and the other will have "x". 



Since the line comes from outside of the face, the line
must go either of its two edges linked with that vertex. And since
this face can have only one line around it, all other edges will be
marked with "x".
Therefore, there are only two possibilities to draw line in this case. 

And the common parts of above possibilities make new rule:
Rule of drawing a line to a corner of "1"  

This rule is also very useful and it is hard to solve puzzles without knowing it.