What is an ideal angle for a seat back piece?
I am sure there are some "standards" but note that there are individual preferences. Take car seats for instance with their range of adjustability. However rear car seats in a sedan or those in many pickup trucks are not adjustable and you may be able to use that as a guide. 

Note that comfort in seating often has the seat bottom sloped down toward the back some too. Case in point would be for you to look at some plans for deck chairs or lawn chairs. The rear sloped seat bottom is especially pronounced in Adirondack style chairs.

Another thing to think about. If the seat base is too long front to back the seat back slope can be extremely awkward for persons with shorter legs. Your pictures give the impression of seat bottoms that may be too deep from front to back for generally comfortable seating.

It may be worth a half day trip to a furniture store and to a home center where deck furniture and lawn chairs are sold. You can learn a lot first hand from what you find comfortable to sit in rather than guessing while drawing away in a CAD program.