I'm designing a build in Bricklink Studio and I need to know which angles a locking hinge plate (newer 7 tooth version) can be set to without the element being put under stress.  I can roughly eyeball it by zooming in, but I prefer to set an exact angle.  I know this information must exist somewhere, but my searching skills are failing me.  Thanks in advance for any help.

I do not have any hinges with 7 teeth. However, the only difference appears to be that the 7 tooth hinges do not have a fourth or sixth tooth (circled below) where the 9 tooth hinges have them. So one would believe that they work with the same angles whether they are 7 or 9 teeth. The difference from one tooth to the next is 22.5 degrees. When one overlays the 9 and 7 tooth hinge part, the teeth are in exactly the same positions.

Brillant.  Exactly what I was looking for.  Thank you.