You wouldn't (locally) be able to measure the angles you have shown on
your figure. You would only be able to measure angles with respect to the local direction of gravity (by, e.g., using a plumbline). The surface of a spinnig selfgravitating sphere, that deforms into an ellipsoid from the rotation, is wellapproximated by a equigravitational potential surface, which means the direction of gravity will be perpendicular to that surface. If you find the points on the respective surfaces where the local plumbline points in your five chosen directions, you'll find the statement in your quote to be true.  Regner Paul Deema wrote:
