If you notice, the section is cut between the teeth.
This means that the dimension doesn't actually go to the angle. If you were to measure that dimension, in that particular section view, you would get something other than 30 degrees. This is because, as the part moves away from the section cut it is also travelling around the diameter.
I believe that this is simply a way for the draftsman to indicate that the angle dimension is specifically on the teeth. It is like a "virtual sharp" almost.
Also, I want to point out that the left side would be a 60 degree countersink tool, while the right side would be a 120 degree countersink tool.
Exactly what I was thinking except described much more clearly by you. I saw the 120° on the other side but forgot to distinguish between the two.