We report an indirect search for nonstandard model physics using the flavor-changing neutral current decays B→K(*)μ+μ-. We reconstruct the decays and measure their angular distributions, as a function of q2=Mμμ2c2, where Mμμ is the dimuon mass, in pp̅ collisions at √s=1.96  TeV using a data sample corresponding to an integrated luminosity of 6.8  fb-1. The transverse polarization asymmetry AT(2) and the time-reversal-odd charge-and-parity asymmetry Aim are measured for the first time, together with the K* longitudinal polarization fraction FL and the muon forward-backward asymmetry AFB for the decays B0→K*0μ+μ- and B+→K*+μ+μ-. The B→K*μ+μ- forward-backward asymmetry in the most sensitive kinematic regime, 1≤q2<6  GeV2/c2, is measured to be AFB=0.29-0.23+0.20(stat)±0.07(syst), the most precise result to date. No deviations from the standard model predictions are observed.