Connecting two PCBs at an acute angle
If you really need to solder it, one way to do this would to get some thick copper sheet metal, like 0.02" or 0.04", and and have a machinist put a bend in the copper at the angle needed. Put some thick pads on the board and solder the copper on. 

The problem with this is you would need a lot of heat for the copper (with it's large thermal mass) which might not be good for the PCB. Pads on the PCB that are used with any kind of mechanical force can result in the pad being ripped from the board, so it's not advisable to use pads for mechanical purposes without strain relief.

It would probably be better to have a piece of metal machined and use fasteners to join the boards together. 

Or you could put holes in the sheet metal and forget the soldering and use fasteners. 

Another good option for fasteners are SMT PEM nuts