To improve upon and provide a methodological alternative to published optoelectronic angle measurement systems, the paper performs high-accuracy angle measurement by use of laser diodes, dual-axis position sensing detectors, and a series of reflections between two first-surface mirrors. Measurement accuracy improves from 0.5 to 0.05 arc sec as the light ray is reflected back and forth several times between the mirrors. Analytic ray tracing is used to model the reflected light ray so as to determine the system equations implicitly in terms of the measured angles. The first-order Taylor series expansion provides a linear form of the system equations. To validate the system, a prototype is built. Calibration and stability experiments are performed. Experimental results show the resolution, accuracy, and measurement range are, respectively, 0.008, 0.05, and ±250 arc sec. Compared with traditional optical angle measurement systems, this method has many merits such as low cost, simple configuration, high sensitivity, and high linearity.