How to find the 120 degree phase angle in a single layered lap winding of a synchronous machine?
What I think is happening...
The motor produces forces from its poles, not its slots.

Now if you trace the U winding, you find it starts (0 degrees) in the first slot - i.e. after the first pole ... and returns (180 degrees) in the sixth slot i.e. just before the 7th pole. 

But keep tracing it ... it starts again in the 12th slot and returns (180 degrees) in the 7th slot. 

Thus the slots either side of the 7th pole are in phase, both 180 degrees. 

Keep tracing the winding and you'll find slots 1 and 24 are both 0 degrees, as are slots 12 and 13, meaning poles 1 and 13 are 0 degrees. Likewise slots 6,7,18,19 are 180 degrees, thus poles 7 and 19.

Repeat for the V and W windings. 

W1 starts in the 5th slot and returns eventually in the 4th slot, both 120 degrees (the 5th pole being 4 * 30 degrees after the first).