What is the standard speed limit on Texas County Roads when not posted?

Boyfriend was pulled over with a claim of the officer of 58 mph. The box on the ticket next to "radar" is unchecked, though. Boyfriend KNOWS he was going 48 mph, but officer claims speed limit is 45 on that County Road. The speed limit is not posted anywhere along the CR. The road is numbered but in an unincorporated area. It is what I'd call "country residential." There are some houses with longer driveways back from the road scattered here and there. There is no shoulder, just a big ditch on either side.

So, if you are in a rural region in Texas on a numbered County Road and there is no speed limit posted, what IS the speed limit? I found the law that states that if it's not posted, the speed limit should be 65 mph. That would be too fast for this road. However, it's not posted anywhere what it actually is. I think he should fight this ticket, but I need a little ammo.