  Consider a collection of points and the sets of slopes or directions of the
lines between pairs of points. It is known that the algebraic matroid on this
set of elements is the well studied 2-dimensional rigidity matroid. This
article analyzes a construction on top of the set of slopes given by an angle
constraint system of incidences and angles. In this setting we provide a
matricial rigidity formulation of the problem for colored graphs, an
algebro-geometric reformulation, precise necessary conditions and a
combinatorial characterization of the generic behaviour for a special case.
