  It is conjectured that every cusped hyperbolic 3-manifold has a decomposition
into positive volume ideal hyperbolic tetrahedra (a "geometric" triangulation
of the manifold). Under a mild homology assumption on the manifold we construct
topological ideal triangulations which admit a strict angle structure, which is
a necessary condition for the triangulation to be geometric. In particular,
every knot or link complement in the 3-sphere has such a triangulation. We also
give an example of a triangulation without a strict angle structure, where the
obstruction is related to the homology hypothesis, and an example illustrating
that the triangulations produced using our methods are not generally geometric.
