Because the solid angle is positioned at the center of the sphere, the edges of the solid angle will intersect the sphere at right angles. That's a mouthful. We need a definition. The plane angles which are the angles, based at the corner, of each plane face of the solid angle, and The dihedral angles which are the angles between two adjacent planes of the solid angle. A, B, and C are plane angles, while D is a dihedral angle.
Dihedral angles can be tricky to visualize.
You measure the dihedral angle between two planes, P1 and P2, of a solid angle by inserting a plane that is perpendicular to the edge between P1 and P2, and then measuring the 2D angle that's cut out on this plane between P1 and P2. Another concept that we can borrow from 2D plane geometry is that of supplimentary angles . In 2D land, you can find the supplimentary angle of an ordinary angle by drawing perpendicular lines from the sides of the angle, seeing where they intersect, and measuring that angle. In the above picture, angle B is the supplimentary angle of angle A. Notice that an angle and its supplimentary angle are complimentary. The below picture might help.