  For an angle $\alpha\in (0,\pi)$, we consider plane graphs and multigraphs in
which the edges are either (i) one-bend polylines with an angle $\alpha$
between the two edge segments, or (ii) circular arcs of central angle
$2(\pi-\alpha)$. We derive upper and lower bounds on the maximum density of
such graphs in terms of $\alpha$. As an application, we improve upon bounds for
the number of edges in $\alpha AC_1^=$ graphs (i.e., graphs that can be drawn
in the plane with one-bend edges such that any two crossing edges meet at angle
$\alpha$). This is the first improvement on the size of $\alpha AC_1^=$ graphs
in over a decade.
