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Three-dimensional (3-D) ray-tracing and analysis is used to characterize the path angles in a rectangular building in which all interior walls are parallel or perpendicular to the exterior walls. Path angles are recorded for 500 random transmitter and receiver locations, maintaining constant range throughout a particular building model. The main contribution of this paper is the observation that when all of the path angles from all 500 trials are measured relative to one building wall and collectively analyzed in a signal strength distribution, clustering is clearly apparent. While this angle clustering in the ensemble of channels is not the same as clustering in a single channel trial, it may partially account for the clusters observed in single trials. As a practical matter, these results may impact the use and placement of directional antennas for wireless LANs in buildings of this type.