Unified schemes attempt to classify radio loud quasars and Fanaroff-Riley Class II radio galaxies as a single type of object, whose properties depend on the orientation of the jet axis relative to the line of sight. We describe a new test of such unification schemes using observed jet opening angles as orientation indicators and apply it to existing data. Opening angles were measured for a subset of the 3CR catalogue, consisting of all identified extragalactic sources with P178 MHz> 10(25) W/Hz and for which high resolution radio maps were found. This provided a sample relatively free of orientation effects. The observed distributions of opening angles for the quasars were compared with those of the galaxies, and with Monte Carlo simulations. We find that the observed jet opening angles of quasars tend to be larger than those of the galaxies; this result is consistent with, and supports, the unified scheme. Detailed Monte Carlo simulations suggest the observations are inconsistent with a simple unified scheme where a single orientation angle sharply distinguishes between quasars and galaxies. We modify Barthel's [ApJ, 336, 606 (1989)] unification scheme by introducing a range of orientation angles that differentiate quasars from galaxies; this yields more consistent results. However, neither Barthel's unification, nor the modification presented here, are fully able to account for the observed differences in quasar and galaxy redshift distributions. Finally, we demonstrate the existence of a loose anticorrelation between jet opening angle and source linear size, confirming that these parameters are useful as orientation indicators.