How to determine phase angle of a three-phase circuit
Now, my main question is how do I work out the phase angle of each
  component?


Draw a phasor diagram: -



In delta, the loads are connected across three line voltage namely Vab, Vbc and Vca. These are shown above on the diagram - they are 120 degrees apart. It's simpler because the three delta loads are all equal and mainly reactive (hence the angle close to 90 degrees). So, for each of the individual line voltages, the current will lag by 76 degrees.

Here's another diagram that is for a delta load of just resistors: -



Important to note is that Ia = Iab - Ica and this tells you how the individual load currents sum to give you the phase current.