  Agol recently introduced the notion of a veering triangulation, and showed
that such triangulations naturally arise as layered triangulations of fibered
hyperbolic 3-manifolds. We prove, by a constructive argument, that every
veering triangulation admits positive angle structures, recovering a result of
Hodgson, Rubinstein, Segerman, and Tillmann. Our construction leads to explicit
lower bounds on the smallest angle in this positive angle structure, and to
information about angled holonomy of the boundary tori.
