Different voltages spliced in same box

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What would be the phase angle between the voltages on the two systems? Once you have that you use the law of cosines or other method of vetor addition to find the voltage between the two.

I understand what you are saying if you have a 277/480 system with a 480V primary to 120/208 secondary. There I could see the picture Smart$ has posted a time or two.
I should have been clearer in my question. If you have a 277/480 service supplied by the POCO, and a seperate 120/240 single phase service supplied from the POCO going to the same building, could the 277 and the 120 have the SAME angle if they are supplied from the same primary phase? And if so, how would that affect the voltages?
 
I am not sure that you would end up with the same phase angle for the secondary of the three phase transformer and the secondary of the single phase transformer, but if you could the voltage between them would be 157 volts. It would be just like measuring the voltage drop across two resistors where the total voltage drop is 277 volts and the drop of one of the resistors is 120 volts.
 
I am not sure that you would end up with the same phase angle for the secondary of the three phase transformer and the secondary of the single phase transformer, but if you could the voltage between them would be 157 volts. It would be just like measuring the voltage drop across two resistors where the total voltage drop is 277 volts and the drop of one of the resistors is 120 volts.

Even with the secondary at -120? would the voltages add to 397? I can't quite figure out how they came up with 380 in the picture.There is no way that is a set voltage. how would you know what angle to measure from? Unless you drew the angle off from the end of the 277 leg...
 
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