Unfortunately fusion does not let you just reference the document axis, you can project an origin plane into the sketch but that's more effort than drawing the Z axis like I did.
In the sketch the document Z is the sketch Y axis, if you sketch a line from the origin you can add a angular dimension from the X axis and Fusion will add the X axis line for you but there's no way to work from the Y without drawing it.

The accuracy you're seeing for the angle is down to the setting in preferences, I'd guess under units you have angular display set to one place. I'm not sure if it's set to display one place and you enter 1.759045 it's rounded or not. The measure tool has a bug when measuring angles and it ignores the setting on the dialog for decimal places and uses the setting in preferences so no quick way to test without going into preferences and experimenting.
Mark
Mark Hughes
Owner, Hughes Tooling
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