Inverted pendulums can be considered as an approximation for the stabilization problem for legged robots. In this paper we design a linear observer for a reaction wheel inverted pendulum under biased angle measurements. The reaction wheel is a flywheel that allows the free spinning motor to apply the control torque on the pendulum. In this paper we consider the stabilization problem in the presence of a constant unknown bias in the pendulum angle measurements; this problem has important practical implications, allowing for less precise sensor placement as well as a closer approximation for the control of legged robots. This paper provides a theoretical and experimental basis for the estimation of the velocities and the bias in the system.