The matroid characterizing the collection of edge lengths in a planar bar-and-joint framework due to Pollaczek-Geiringer, and rediscovered by Laman, is widely-celebrated. Less heralded is the fact that the edge directions (or bearings) of a planar framework define the same matroid. This result goes back to a 1987 book chapter by Whiteley and was reproved in 2003 by Martin using algebraic geometry. Their techniques give insight into an even less-studied matroid defined by angles between pairs of edges. In this talk, I will discuss some new results about that angle matroid, and describe some angle analogs of rigidity-theoretic concepts like circuits and the pure condition. This is based on work with Sean Dewar, Georg Grasseger, Anthony Nixon, William Sims, Meera Sitharam, and David Urizar. I will also report on new computational work, joint with Sophie Faris, to analyze all angle configurations on five vertices.