Measurements of CP observables in B±→D(⁎)K± and B±→D(⁎)π± decays are presented, where D(⁎) indicates a neutral D or D⁎ meson that is an admixture of D(⁎)0 and D¯(⁎)0 states. Decays of the D⁎ meson to the Dπ0 and Dγ final states are partially reconstructed without inclusion of the neutral pion or photon, resulting in distinctive shapes in the B candidate invariant mass distribution. Decays of the D meson are fully reconstructed in the K±π∓, K+K− and π+π− final states. The analysis uses a sample of charged B mesons produced in pp collisions collected by the LHCb experiment, corresponding to an integrated luminosity of 2.0, 1.0 and 2.0 fb−1 taken at centre-of-mass energies of s=7, 8 and 13 TeV, respectively. The study of B±→D⁎K± and B±→D⁎π± decays using a partial reconstruction method is the first of its kind, while the measurement of B±→DK± and B±→Dπ± decays is an update of previous LHCb measurements. The B±→DK± results are the most precise to date.