polyhedra: total angle sum

Euler's relationship connecting the numbers of faces, edges and vertices (F + V is close to E) for polyhedra is fairly well known

another (very neat) relationship for the 'total angle sum' was brought to my attention by Gordon Haigh, when he worked at Wolverhampton University

a powerpoint for this task gives the steps for proofs for a general prism and general pyramid, establishing Euler's  relationship for these polyhedra

animated platonic solids from Wikipedia: