Fp2 chapter 3 Loci of complex numbers question

Hi, I'm having some problems with the questions in fp2, an example of one would be:
sketch the locus of z when:arg (z-3i) - arg(z-5) = pi/4
in the example in the book, it says to do:

let arg (z-3i) = theta (i cant find the symbol)
arg (z-5) = alpha

theta - alpha = pi/4

then draw both individually on an argand diagram, and the loci is the circle round the points where they intersect.

In mostly okay with that I think, but what I don't understand is sometimes the line they draw for arg (z- whatever) has a positive gradient, and sometimes it has a negative gradient - i.e. sometimes they take theta to be obtuse and sometimes they take it to be accute, and the same for alpha.
How do you know whether theta/alpha is accute or obtuse, or when to use negative theta/alpha on your diagram?

Sorry I know I havent explained it very well but can anyone help?