TITLE: What is this angle calculation rule with $2$ parallel lines?
QUESTION [5 upvotes]: The rule is that when line n and m are parallel, 
$$b=a+c$$
What's the name of this rule? - You won't believe how many books I've checked.

REPLY [6 votes]: One that comes close is the exterior angle theorem that gives $\,b=a+c\,$ in the construction below: