The angular distributions and the differential branching fraction of the decay B0 to K*(892)0 mu+ mu- are studied using a data sample corresponding to an integrated luminosity of 5.2 inverse femtobarns collected with the CMS detector at the LHC in pp collisions at sqrt(s) = 7 TeV. From more than 400 signal decays, the forward-backward asymmetry of the muons, the K*(892)0 longitudinal polarization fraction, and the differential branching fraction are determined as a function of the square of the dimuon invariant mass. The measurements are in good agreement with standard model predictions.