Good morning Engrs.
It is true that the phase angle in electrical system is gotten by 360° divided by the number of phases then, Why is that the phase angle of a 2-phase system is 90° instead of 180°

 

That's what "they" decided to do. See https://en.wikipedia.org/wiki/Two-phase_electric_power

In a "two phase" system, power is INDEPENDENT and delivered on 2 pairs of wires.

If they were 180 degrees out of phase, you would have a harder time rotating a motor. If you had a winding at say 120 V and the other at zero, I don;t think there would not be a tendency to want to rotate.

A funky picture. Pretend there is an Auger in the dirt with a long "T" type handle and two people pushing the ends of the stick. At 180 deg out of phase, one guy would not be doing any work turning the auger. They would be pushing with a sine wave type of force.


The difference in phase would seem to be arbitrary.