59 quasars in the background of the Magellanic Clouds had brightness records monitored by the MACHO project during the years 1992–99. Because the circumpolar fields of these quasars had no seasonal sampling defects, their observation produced data sets well suited to further careful analysis. Following a preliminary report wherein we showed the existence of reverberation in the data for one of the radio-quiet quasars in this group, we now show that similar reverberations have been seen in all of the 55 radio-quiet quasars with adequate data, making possible the determination of the quasar inclination to the observer’s line of sight. The reverberation signatures indicate the presence of large-scale elliptical outflow structures similar to that predicted by the Elvis and ‘dusty torus’ models of quasars, whose characteristic sizes vary within a surprisingly narrow range of scales. More importantly, the observed opening angle relative to the polar axis of the universal elliptical outflow structure present was consistently found to be on the order of 78°.