Cut a piece of 7 3/4-by-29-inch 3/4-inch plywood in half diagonally using a saw, so you have two triangular pieces of plywood, with a 90-degree angle between the 7 3/4-inch and 29-inch sides, a hypotenuse of 30 inches and the remaining corners 15 and 75 degrees.
Lay a sheet of 7 3/4-by-35-inch plywood flat on the work surface. Abut the two triangles on either end, with the 7 3/4-inch sides of the triangles abutting the 7 3/4-inch sides of the flat plywood piece.
Glue the triangles in place, then secure with four evenly spaced 1 1/4-inch screws through the 7 3/4-inch edge of the triangles into the 7 3/4-inch end of the flat panel of plywood.
Paint the flat panel and attached triangle brackets, as well as two planks of 35-inch 2-by-2 lumber and a piece of 30-by-40-inch plywood, which is the desktop. Leave to dry.
Lay the panel with the triangle brackets attached flat on the work surface and place the two 2-by-2 planks onto the flat panel, one flush with the top edge, one with the bottom edge. Glue in place.
Locate the position of your wall studs where you want to install the desk and draw a level line between them 40 inches long, to represent the desk position. The line should be roughly 28 to 30 inches off the ground, the most common desk heights.
Position the panel with the triangles attached on the wall line, with the 7 3/4-inch side of the triangle flush against the wall, and the 29-inch side horizontal, or perpendicular to the wall.
Secure the panel to the wall with two 4-inch screws driven through the two 2-by-2 lumber planks at every wall stud point.
Place the desktop panel over the 30-inch side of the triangle brackets. You will have an inch overlap at the front of the desktop, and a couple inches over each side. Secure with 1 1/4-inch screws through the desktop into the 30-inch side of the triangle brackets.
Fill the head of all the visible screw holes with wood putty, then touch up with paint to finish the angled desk.