I think you need to use an auxiliary fence (parallel strip of material, with a thickness equal to or thinner than the piece you're cutting), you can cut the auxiliary fence at an angle, so you'll have support at the guiderail, but it doesn't have to go past the bracket with the hinge. The width would have to be wide enough so the material you're cutting will slide past that bracket.
Personally I haven't used my mft for cuts other than 90 degrees, if I would have to cut something at such a sharp angle and it's too wide for my SCMS (or the angle too sharp), I would go for the angle guide on the guiderail (I have 2 different versions, the festool version and a protool version)