Okay that is kind of what I ended up doing except instead of rotating the tubes I just rotated the box beneath them Then extruded both tubes, intersected them with the model and then erased the parts sticking up and the top surface of the box circumscribed by the circles. Viola I now have two holes in the box at the same correct angle. Sorry I didn't figure this out sooner from you guys examples but, I just couldn't connect the dots on this one. Thanks for all your help though. I will definitely remember this the next time I need an angled hole in a surface.
Z