[Tristan Lall]

I don't have Inventor in front of me now, but what about creating a work plane at an angle to the existing surface? Then sketch the outline of the hole in the workplane and create a feature, setting the depth to whatever you need (through to reverse side). To be honest, I don't remember if Inventor will let you create a solid material removal feature (i.e. hole or cut) from a workplane in space, but it's worth a shot.

Also, since you may want to actually build the thing later, be aware that it is tricky to drill an angled hole. You'd either need a drill guide (some hard material which already has the desired angled hole), or a very stiff machine, like a milling machine and a short, inflexible bit or end mill. Even if you tilt the table of a drill press, the bit will usually walk off and make a mess.