Due to the efficiency and accuracy, the visual measurement method based on circular features is widely used in computer vision applications. However, the duality problem interferes the process of monocular vision pose estimation with a single circle feature. In order to exclude of the false solution effectively, a method utilizing angular constraint to solve the ambiguity is proposed based on the attitude estimation with the three lines configuration. For a known three lines configuration, an angular constraint about the normal vector of the single circle is deduced with the attitude between the configuration and the camera coordinate. If the three lines configuration is unknown, an angular constraint between the normal vectors of the circle in two camera views is deduced with the relative attitude estimation with a pair of matched three lines configuration. Both of the angular constraints can be applied to exclude the false normal vector of the circle. Experimental results indicate that the proposed approach can effectively solve the duality problem. The success rate is up to 99.2% for the first angular constraint, and the success rate is up to 96.7% for the second angular constraint.