Okay, how bout this. If you have a vertical surface, and want to drill a hole into that surface at 10 degrees off-chamber (so to speak), you can create a plane that is 10 degress off the vertical surface, and place your hole there. Same way as a cut I'm thinking.
Now your problem is only where exactly the hole will be in the vertical face, if the 10 degree plane is offset from it. So, maybe you place a 3dsketch in there, and "align" the vertical face point of the line to the vertical face, and make it perpendicular to the angled plane. Then "align" hole to the 3d line.
Maybe this gets you going, or thinking, or worse....
Mr. Pickles