The production properties of dijets from pbar p collisions at sqrt
s = 1.8 TeV have been studied using the Collider Detector at Fermilab.  This
report presents an analysis of the dijet angular distributions using 106 pb^-1
of data collected during Run I of the Tevatron Collider.  The measured angular
distributions agree with next-to-leading order QCD predictions in five dijet
invariant mass regions with average dijet mass varying from 263 to 698
GeV/c^2.  The predicted angular distributions are relatively insensitive to
parton distribution functions, and therefore these data can be used to put
limits on energy scale parameters used to describe contact interactions.  For
a model with only up and down quarks composite, the data exclude at 95%
confidence level a contact interaction scale Lambda^+_ud \leq 1.6 TeV or
Lambda^_ud \leq 1.4 TeV.