This study determines the sensitivity of human observers to 2D fronto-parallel angles. Angle discrimination thresholds vary as a function of base angle and stimulus configuration orientation. However, these variations can all be understood from the well-known meridional anisotropy for orientation discrimination of the orientations that define the angle. Specifically, observers do not show any special sensitivity to angles of 90 degrees and 180 degrees (straightness). Instead it is claimed that observers measure geometric angle by comparing the visual orientations that define the angle, although it is shown that they are not fully efficient in this comparison operation. An explicit visual reference angle does not improve discrimination thresholds (that is, observers can perfectly well supply one from memory), nor do observers need an explicit visual reference orientation in an orientation discrimination task.