  The angular resolution of a planar straight-line drawing of a graph is the
smallest angle formed by two edges incident to the same vertex. Garg and
Tamassia (ESA '94) constructed a family of planar graphs with maximum degree
$d$ that have angular resolution $O((\log d)^{\frac{1}{2}}/d^{\frac{3}{2}})$ in
any planar straight-line drawing. This upper bound has been the best known
upper bound on angular resolution for a long time. In this paper, we improve
this upper bound. For an arbitrarily small positive constant $\varepsilon$, we
construct a family of planar graphs with maximum degree $d$ that have angular
resolution $O((\log d)^\varepsilon/d^{\frac{3}{2}})$ in any planar
straight-line drawing.
