Can I support an extra 10 inches of sub floor overhang with 2x10 angle pieces bolted to the side of a joist? It'd be a 6 foot run. I figure I'd space the angle pieces 10 to 12 inches apart and secure them together with 2x6s in between laid horizontally in between. I need to extend a non structural wall so I can extend a bathroom wall out approximately 10 inches.
If you look at the picture I added to this post, I'd basically do that.
Side A would be the joist and side B would be my sub floor
No.
Any cantilever needs a 1:3 overlap ratio at minimum. That means a girder joist inside the existing floor three times the overhang depth, a beam at (underneath) the edge of the existing floor, and perpendicular joists. You cannot apply twisting forces to the rim joist as you propose.
Even if you fully boxed the existing joists against twist, you're relying on fasteners in tension. That's rarely allowed. You need direct bearing and fasteners working in shear. The fact that you're triangulating with the subfloor is irrelevant. That's not a structural technique any inspector would allow.
I suggest that your reformulate your question to ask how to solve your problem rather than posing the XY question you have now.
