Is it possible to use prefab fence sections to fence in a trapezoid shaped area, where the corners are greater than 90 degrees? How would I do it? Or is my only option to construct the fence from scratch? Then what would I do? I have been researching this for weeks and all the sources I have consulted only address 90 degree corners.

My dream fence would be a white vinyl picket. Wood pickets are my second choice. Split rail seems more accomodating, but doesn't really work with the neighboring fences we have to tie into. We are the unfenced lot between two fenced lots. Thanks for your help.

If you really want white vinyl, I doubt any maker produces a universal corner that will fit any angle. Nor would they produce just the precise angle you need - there's not a market for one-of-a-kind angle pieces.
Depending on the makeup (size, shape, style) of the vinyl pieces, maybe you could make your own wood angle pieces and paint them to match the vinyl. If you do that, I suggest cedar.
Another option is to not use corner pieces at all. Simply "stop" the fence at the corner from both directions, with the two "ends" touching.