This angle right here should give me the angle between the neck and the body. I need that angle to correctly cut out the neck pocket.
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I suggest you talk to a luthier who is experienced with neck resets.
He could give you the angle you need.
[Unless this is a really old guitar, the angle you need should be pretty much standard, as fingerboards are mass produced (and are the same), so stop lengths (and neck angles) are the same.]
the angle on the pickup may be right for the guitar neck, but I would not trust it. A slight error on the neck/mortise joint makes a lot of difference.
For a violin anyway, and probably guitar, the way to do this is; the mortise in the neck block is cut flat and true with the rib assembly (of the corpus, or body of the guitar/violin).
Then all of the neck angle is cut on the heel (of the neck).
and you fine tune the neck set via the cut on the heel.
[the heel is much easier to work with than the mortise.]
for the geometry problem you presented, Dr. Peterson gave the solution.