One type of phased-array radar of current interest employs an array of separate receiving elements, each followed by an individual amplifier. These individual signals are combined coherently to form one or more receiving beams for searching, tracking, or performing both functions simultaneously. This paper presents an approach to the theory of angle measurement with a phased array of this type. In the one-dimensional problem considered here, the receiving antenna consists of a linear array of individual antenna-amplifier elements. The receiver-noise-limited case is considered, in which accuracy is limited by the additive normally distributed noise present in each channel. An expression is derived for the limiting accuracy of angular measurement when a single set of samples is available. This set of samples is obtained simultaneously, one sample from each channel. Next, two methods of implementing the angular measurements are discussed. These are amplitude comparison monopulse and a coherent or phase comparison technique. For large signal-to-noise ratios and for either a square law or a linear envelope detector, the accuracy of amplitude comparison monopulse approaches the theoretical limit. The same accuracy can be achieved with the coherent technique by proper weighting of the individual signals.