How can you cut a rectangular cake, with a rectangular slice (of any size/orientation) taken out, into two equal halves? You can only make one straight cut from the top of the cake (ex. cutting the cakes' height in half is not allowed).
Through what point must you cut any single rectangle in half?
Cutting a rectangle through its center with one straight cut will always result in two equally sized pieces. By cutting our cake through the centers of both rectangles (center of the cake as a whole and the center of rectangular slice taken out), we are guaranteed two equally sized slices.