Constraint-based CAD software, used by engineers to design sophisticated mechanical systems, relies on a wide range of geometrical constraints. In this paper we focus on one special case: angular constraints in 3D. We give a complete combinatorial characterization for generic minimal rigidity in two new models: lineplane-and-angle and body-and-angle structures. As an immediate consequence, we obtain efficient algorithms for analyzing angular rigidity. pairwise angular constraints between them. A body-andangle structure is composed of rigid bodies with lines and planes rigidly affixed to them; angular constraints are placed between identified lines or planes on a pair of bodies. See Figures 1a and 2a for examples. We restrict the angular constraints to lie in the range [0, π] and remark that this restriction does not limit our model, as an angle α larger than π may be associated to the “small ” angle 2π − α. For lack of space, we present here only the (0, π) case. 1