The first full angular analysis and an updated measurement of the decay-rate CP asymmetry of the D0 ??? x-+x-?????+????? and D0 ??? K+K?????+????? 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.