Everyone learns in school that the measures of the angles in a euclidean triangle add up to pi.  Are there corresponding restrictions on the dihedral angles and/or solid angles in a tetrahedron? In this talk I will describe some basic results on angles in high-dimensional polytopes and the various equations they satisfy. To be able to state these classical results (due to Sommerville and MacMullen) I will also introduce the notion of the incidence algebra of a poset as well as moebius inversion and zeta functions.