In this paper, we investigate the vanishing micro-rotation and angular viscosities limit of solutions to the 2D incompressible micropolar equations in a bounded domain with Navier-type boundary conditions satisfied by the velocity field. In a general bounded smooth domain Ω , we establish the uniform H 2 (Ω) estimates (independent of the micro-rotation and angular viscosities) of global strong solutions and prove the rate of convergence of viscosity solutions to the inviscid solutions in C (0 , T ; H 1 (Ω)) for any T > 0 . [ABSTRACT FROM AUTHOR]