I'd bet a 60,,or something very close to that. Most of the tools were hand made or in the least resharpened many times by the user over time and lost their precise original angle.

I'd steam it first as already mentioned.
Wet the area with a Q-Tip w/water to get some water into the wood first.
Then with a small cloth patch dampened w/water placed over the spot,,press down on it with an electric soldering gun for quick heat & steam to just the right area.

The water soaked into the wood already will turn to steam and raise what fibers it can. It'll be bone dry in a few seconds after the treatment,,so adding more won't hurt if you think it'll help towards the goal.

There's always a chance it's been cut w/a 90. But I doubt it.

Start w/a 60. You can always improve it,,even using the same 60 by carefully tilting it to the side in touching up the small damaged area.
Hard to go back and make the diamonds narrower once you cut it with the wide tool first.

The area will probably need a touch of 'age and wear' when done to match the overall pattern well. Some 'crud' in the lines always helps too.