  Let M be the interior of a compact 3-manifold with non-empty boundary, and T
be an ideal (topological) triangulation of M. This paper describes necessary
and sufficient conditions for the existence of angle structures, semi-angle
structures and generalised angle structures on (M; T) respectively in terms of
a generalised Euler characteristic function on the solution space of normal
surface theory of (M; T). This extends previous work of Kang and Rubinstein,
and is itself generalised to a more general setting for 3-dimensional
pseudo-manifolds.
