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One of the fundamental issues in sensor networks is the coverage problem, which reflects how well a field is monitored or tracked by sensors. Various versions of this problem have been studied, such as object, area, barrier, and hole coverage problems. In this paper, we define a new k-angle object coverage problem in a wireless sensor network. Each sensor can only cover a limited angle and range, but can freely rotate to any direction to cover a particular angle. Given a set of sensors and a set of objects at known locations, the goal is to use the least number of sensors to k-angle-cover the largest number of objects such that each object is monitored by at least k sensors satisfying some angle constraint. We propose centralized and distributed polynomial-time algorithms to solve this problem. Simulation results show that our algorithms can be effective in maximizing coverage of objects. A prototype system is developed to demonstrate the usefulness of angle coverage.