Were you creating that 'Dimension' in the context of a Drawing or as part of a Parametric Sketch, which is what the OP was asking for?
One option would be to create a reference line in the sketch and create the angular dimension between the line and reference line. The circle can be constrained to the end point of the reference line.
This is indeed the only way to do it. Create a reference line from the origin of the sketch. In NX 11.0.1 the reference line will be invisible when you finish the sketch.
Thanks for all the responses.
Yes, my question was in regard to the sketch environment (not draft, which appears to have more options for doing this).
I knew I could use a reference line, which is probably a clearer way of doing this. But I generally like to keep my sketches as uncluttered as possible, so was wondering if I could avoid that. Not a big deal, but would be a nice feature for NX to have at some point. I actually used it a lot in SE.