  We have used 106 pb^-1 of data collected in proton-antiproton collisions at
sqrt(s)=1.8 TeV by the Collider Detector at Fermilab to measure jet angular
distributions in events with two jets in the final state. The angular
distributions agree with next to leading order (NLO) predictions of Quantum
Chromodynamics (QCD) in all dijet invariant mass regions. The data exclude at
95% confidence level (CL) a model of quark substructure in which only up and
down quarks are composite and the contact interaction scale is Lambda_ud(+) <
1.6 TeV or Lambda_ud(-) < 1.4 TeV. For a model in which all quarks are
composite the excluded regions are Lambda(+) < 1.8 TeV and Lambda(-) < 1. 6
TeV.
