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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.

image illustration

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    $\begingroup$ 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. $\endgroup$
    – egreg
    Dec 15, 2017 at 7:24

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

enter image description here

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  • $\begingroup$ That was what I was thinking too $\endgroup$
    – Mark Bennet
    Dec 15, 2017 at 8:06
  • $\begingroup$ and why the angles a abd a-red are equals? $\endgroup$
    – user
    Dec 15, 2017 at 9:09
  • $\begingroup$ @gimusi that's called the Z rule $\endgroup$
    – csg
    Dec 15, 2017 at 10:00
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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.

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