This paper investigates how to maneuver a planar formation of mobile agents using designed mismatched angles. The desired formation shape is specified by a set of interior angle constraints. To realize the maneuver of translation, rotation and scaling of the formation as a whole, we intentionally force the agents to maintain mismatched desired angles by introducing a pair of mismatch parameters for each angle constraint. To allow different information requirements in the design and implementation stages, we consider both measurement-dependent and 10 measurement-independent mismatches. Starting from a triangular formation, we consider generically angle rigid formations that can be constructed from the triangular formation by adding new agents in sequence, each having two angle constraints associated with some existing three agents. The control law for each newly added agent arises naturally from the angle constraints and makes full use of the angle mismatch parameters. We show that the control can effectively stabilize the formations while simultaneously realizing maneuvering. Simulations are conducted to validate the theoretical results.