[math-fun] Four solid angles

How many of you already know (or can figure out) what four solid angles associated with a general tetrahedron add up to 4 pi? I've been told that George Polya, when asked, replied with the correct answer instantly (it was part of his geometric toolkit), but that few of his contemporaries, when polled in an informal survey, were aware of this three-dimensional analogue of the familiar fact about the angles of a triangle summing to pi. I'm guessing that things haven't changed much in the intervening half-century. Jim Propp