I am building a 24x30 cabin,the roof will lay on the 30 ft side,and there will be a loft,the loft I want to have clearance of a least 7 ft,I want to use 2x6x20 for the roof,but I need to know what angle should I cut the 2x6x20 to get this pitch??

Gable style would only need 2- 16' rafters (2' overhangs). Get yourself a rafter square. See Trigonometry Angle Calculator - Online Interactive Visual Triangle Calculator (http://www.visualtrig.com) to find angles otherwise.

OnTheMark gave you a great tool but I have some questions for you. I have work on several cabins and log homes and just wonder what you plan to do with a loft with less than 8' clearance at the peak. Most lofts, if you plan to do any living space, start with a peak of 12' so you have a decent sized room with a 8' ceiling. Tell us more. I just finished a 22x30' garage and the peak was 11' giving me a finished loft 9' wide with an 8' ceiling.