Metasurfaces are versatile electromagnetic structures for wave shaping, yet their angular dispersion remains underexplored. Using generalized sheet transition conditions (GSTCs), we analyze metasurface angular dispersion and derive conditions for angle-invariant co- and cross-polarized transmission and reflection, where amplitude, phase, or both remain unchanged with incidence angle. We reveal that nonlocality can suppress angular dispersion, enabling complete angle-invariant scattering. Additionally, we show that pseudochiral metasurfaces can achieve efficient extrinsic chirality in a partially angle-invariant manner. These results provide a strategy to mitigate angular-dependent scattering, essential for applications sensitive to dispersion effects.