# What is this angle calculation rule with $2$ parallel lines?

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.

• I’ve never seen a name for this theorem, which is a standard corollary of the main theorem on parallel lines cut by another line. – egreg Dec 15 '17 at 7:24

One that comes close is the exterior angle theorem that gives $\,b=a+c\,$ in the construction below:
I don’t think there exists a name for this theorem. You can solve it by taking a line parallel to both lines $m$ and $n$, through the vertex of the crook between the lines.