Your going to want to attach the two new walls to the existing walls using the first stud of the new wall. Your top plate will attach to that wall stud which has been attached to the existing wall. Where the corner of the two new walls meet, you'll want to run a stud on a 45 degree angle, tying the two new walls together at the top plate. One thing I tell my guys is to look at the big picture (legal egress, carpeting, mop board, HVAC, fire supression, wall outlets, separate lighting, etc....). Good Luck.