  A Monte Carlo study of the polar and azimuthal angular distributions of the
lepton pair arising from the decay of a $W$ or $Z$ boson produced at high
transverse momentum in hadronic collisions is presented. In the absence of cuts
on the final state leptons, the lepton angular distribution in the gauge boson
rest frame is determined by the gauge boson polarization. Numerical results for
the lepton angular distributions in the Collins--Soper frame with acceptance
cuts and energy resolution smearing applied to the leptons are presented. In
the presence of cuts, the lepton angular distributions are dominated by
kinematic effects rather than polarization effects, however, some polarization
effects are still observable on top of the kinematic effects. Polarization
effects are highlighted when the experimental distributions are divided by the
Monte Carlo distributions obtained using isotropic gauge boson decay.
