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Is the neck angle determined by the angle the scarf joint is cut at?

I ask because I was just looking at a seagull 12 string I have, the angle seems to measure at 16 degrees, however Seagull's literature online says the scarf joint is cut at 45 degrees. Logic, the Campiano book, and my experiment with scrap seem to say that there is no way I should be able to get that 16 degree angle out of a cut made at 45 degrees. So is the head stock angle actually carved into the neck after the fact?

If the 15-16 degree headstock angle were carved into a joint that was glued at 45 degrees, you would undo any good that came from making the scarf joint. The scarf joint is useful because the headstock can be made out of straight grain wood, instead of cross grain wood. So, yes, the headstock angle should match the scarf joint angle. You cut it at 15 degrees, thin the headstock to the right thickness, flip it over, and glue it on the back of the neck (per the illustrations on the Seagull website).

I think the Seagull online stuff merely has a typo in it. A copy editor probably doesn't care about the difference between a 15 degree and a 45 degree angle.

I would not call it a neck angle, by the way, because that will just cause confusion. The neck angle normally refers to the 1-1.5 degree setback of the neck at the neck/body joint. Completely different angle.

Oops, right I knew that about the head stock, neck angle thing. That makes sense about the typo too, I suppose its the only solution that makes sense of their diagram.