The angles your asking about are not really what matters so much in that the dimensions you have determine what the angle are. But, without a frame of reference as to what the measurements are from a 90 degree square point, the lengths of each dimensions make determining the those angles difficult.
What you could do is use Google SketchUP to create each dimension length and then rotate each line to connect to the others based on their lengths.
Don't change the length of the lines, you'll have to keep adjusting the degree of angle till all lines connect to re-create that which you are doing from the pictures.
I know that's not the college answer you looking for, but, given the info available, that is the way I would try to do it and tweak the design in sketchup to get it close as possible.
