I would use edge slide to tackle this. In edit mode, select a line, tap ‘G’ twice to go into edge slide mode and slide the lines together. Then tap ‘A’ to select the whole mesh, tap ‘W’ to go to the specials menu and select ‘remove doubles’ (to avoid overlapping vertices). I would start with the bigger lines on the side, working your way from outside to the inside. When they are done you can slide the remaining vertices on the top and/or bottom to the corner. That should give you a sharp 90 degree corner. I haven’t been using Blender for long, so maybe one of the more experienced people here knows a faster way, but that is how I would do it. Hope this helps!
