Phase Angle

I have a transformer with a 480v single phase input and 120/240 taps. It was a leftover from another project at the same building.
Evidently it was fed with two legs of a 480v three phase supply, which is what's all over the building. I'd like to do the same in another location in the same building.
What confuses me is the phase angle. The way I understand it, a three phase circuit has the phases 120 degrees apart, while a single phase is 180 degrees.
With just two legs of a three phase supply, won't the phases be, um, out of whack? Will this harm motors or do any wierd things with other appliances?
I must be missing something. Anyway, I don't plan on installing this myself. I'll be getting a qualified electrician for all that. The reason I ask is I don't want to install something that will start killing whatever I connect to it.
The plan is to install this into the boiler room. It'll be running large pedestal fans, lights, water softener systems, and the occasional power tool. Right now it's fed with a 208v with a boost to bring it up to 230, and a standard 110v circuit. Unfortunately, the closest transformer on the floor is on the other side of the building, so I'm getting voltage drops between 5 and 10 percent. There's a 480 box inside the boiler room, and I'm converting everything I can to run off that, but it's just not practical with everything.
Thanks in advance.
CS
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