3/4" plywood base that is 2" longer front to back than the bottom of the "laptop" needs to be.
1/4" luan plywood back for screen.
1/4" wide groove cut in plywood base to accept 1/4" luan.
glue luan into groove, and if have access (which any well equipped wood shop should) tack with 1/2" long brads (pneumatic air gun).
cut the groove at a 30degree angle as measured on the backside of the screen --- this best done by using a table saw with the blade set at 30 degrees and the fence up close to the blade about 2" or so.
(although the image name says cell phone base, it's the exact same set up just different overall shape for laptop. The extra 2" extends past the back of where the luan slots into base to give extra stability)