To realize high precision angle measurement on a scanning control machine, taking an absolute round inductosyn as the angle measuring sensor, a high precision and high stability angle measuring system is designed. Through the design of hardware circuits and FPGA program, high precision and high stability angle measurement and high reliability absolute angle measurement are achieved respectively. The actual experimental results show that the system has strong anti-interference ability. Its stable angle resolution is up to 0.1'' and its angle pointing accuracy is better than 1.1'' (3σ).