Simple center finder.
Step 1: MDF
Cut two pieces of MDF.
Step 2: Glue
Glue and clamp them at a right angle.
Step 3: Screw
Reinforce the joint with screws and check for square.
Step 4: Angle
Cut a right angled triangle piece of MDF.
Step 5: Glue
Glue and clamp in place.
Step 6: Pivot Screw
Before the glue dries insert one screw to reinforce and to pivot. Check the 45 degree angle and adjust appropriately, then insert a second screw.
Step 7: Seal
Seal the edges of the MDF with glue and give the piece a coat of shellac to prevent moisture from warping the shape.