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The rule is that when line n and m are parallel,
What's the name of this rule? - You won't believe how many books I've checked.
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.