The first full angular analysis and an updated measurement of the decay-rate CP asymmetry of the D^{0}→π^{+}π^{-}μ^{+}μ^{-} and D^{0}→K^{+}K^{-}μ^{+}μ^{-} decays are reported. The analysis uses proton-proton collision data collected with the LHCb detector at center-of-mass energies of 7, 8, and 13 TeV. The dataset corresponds to an integrated luminosity of 9 fb^{-1}. The full set of CP -averaged angular observables and their CP asymmetries are measured as a function of the dimuon invariant mass. The results are consistent with expectations from the standard model and with CP symmetry.