  The Erd\H{o}s distinct distance problem is a ubiquitous problem in discrete
geometry. Less well known is Erd\H{o}s' distinct angle problem, the problem of
finding the minimum number of distinct angles between $n$ non-collinear points
in the plane. The standard problem is already well understood. However, it
admits many of the same variants as the distinct distance problem, many of
which are unstudied.
  We provide upper and lower bounds on a broad class of distinct angle
problems. We show that the number of distinct angles formed by $n$ points in
general position is $O(n^{\log_2(7)})$, providing the first non-trivial bound
for this quantity. We introduce a new class of asymptotically optimal point
configurations with no four cocircular points. Then, we analyze the sensitivity
of asymptotically optimal point sets to perturbation, yielding a much broader
class of asymptotically optimal configurations. In higher dimensions we show
that a variant of Lenz's construction admits fewer distinct angles than the
optimal configurations in two dimensions.
  We also show that the minimum size of a maximal subset of $n$ points in
general position admitting only unique angles is $\Omega(n^{1/5})$ and
$O(n^{\log_2(7)/3})$. We also provide bounds on the partite variants of the
standard distinct angle problem.
