I am working in a project where high precision of angles is needed. I have set Rhino properties to use 0.01° (which is the highest) in a meter file. I am not seeing any options in Grasshopper, but after messing around with it I am fairly confident that the angle precision rounds up/down at 3 decimals.
this controls how close Rhino has to get when considering things like whether two lines are parallel. It doesn’t control precision when setting, measuring or displaying an angle.
Here’s an example where Rhino is displaying an angle of 22.000001°, and Grasshopper has rotated a curve by 30.000000001° and measured and displayed that angle to the same nine decimal places:
Rhino display precision is set in the Annotation Style you employ; Grasshopper display precision is set in the text formatting as shown by Anders above. Measurement precision is seemingly adequate to support these extreme values.