  This paper describes a way to subdivide a 3-manifold into angled blocks,
namely polyhedral pieces that need not be simply connected. When the individual
blocks carry dihedral angles that fit together in a consistent fashion, we
prove that a manifold constructed from these blocks must be hyperbolic. The
main application is a new proof of a classical, unpublished theorem of Bonahon
and Siebenmann: that all arborescent links, except for three simple families of
exceptions, have hyperbolic complements.
