Measurements of $CP$ observables in $B^\pm \rightarrow D^{(*)} K^\pm$ and $B^\pm \rightarrow D^{(*)} \pi^\pm$ decays are presented, where $D^{(*)}$ indicates a neutral $D$ or $D^*$ meson that is an admixture of $D^{(*)0}$ and $\bar{D}^{(*)0}$ states. Decays of the $D^*$ meson to the $D\pi^0$ and $D\gamma$ 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 $K^\pm \pi^\mp$, $K^+ K^$ and $\pi^+ \pi^$ 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 centreofmass energies of $\sqrt{s}$ = 7, 8 and 13 TeV, respectively. The study of $B^{\pm} \to D^{*} K^{\pm}$ and $B^{\pm} \to D^{*} \pi^{\pm}$ decays using a partial reconstruction method is the first of its kind, while the measurement of $B^{\pm} \to D K^{\pm}$ and $B^{\pm} \to D \pi^{\pm}$ decays is an update of previous LHCb measurements. The $B^{\pm} \to D K^{\pm}$ results are the most precise to date.
Invariant mass distributions of selected $ B ^\pm \rightarrow [ K ^\pm \pi ^\mp ]_{D}h^{\pm}$ candidates, separated by charge, with $ B ^ {\rm(} B ^+ {\rm)}$ candidates on the left (right). The top panels contain the $ B ^\pm \rightarrow D^{(*)0}K^{\pm}$ candidate samples, as defined by a PID requirement on the companion particle. The remaining candidates are placed in the bottom panels, reconstructed with a pion hypothesis for the companion. The result of the fit is shown by the thin solid black line, and each component is listed in the legend. The component referred to as `Part. reco. misID' is the total contribution from all partially reconstructed and misidentified decays. 
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Invariant mass distributions of selected $ B ^\pm \rightarrow [ K ^+ K ^ ]_{D}h^{\pm}$ candidates, separated by charge. See Fig. 1 for details of each component. 
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Invariant mass distributions of selected $ B ^\pm \rightarrow [\pi ^+ \pi ^ ]_{D}h^{\pm}$ candidates, separated by charge. See Fig. 1 for details of each component. 
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$1\sigma$, $2\sigma$ and $3\sigma$ profile likelihood contours for $r_{B}^{D^{*} K}$, $\delta_{B}^{D^{*} K}$ and $\gamma$, corresponding to 68.3%, 95.5% and 99.7% confidence level (CL), respectively. The contours are measured using $ B ^ \rightarrow ( D \pi ^0 )_{ D ^* } K ^ $ and $ B ^ \rightarrow ( D \gamma)_{ D ^* } K ^ $ decays. The colour scale represents $1\text{CL}$. 
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Animated gif made out of all figures. 
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Systematic uncertainties for the $ C P$ observables measured in a partially reconstructed manner, quoted as a percentage of the statistical uncertainty on the observable. 
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Systematic uncertainties for the $ C P$ observables measured in a fully reconstructed manner, quoted as a percentage of the statistical uncertainty on the observable. The Sim uncertainty on $R_{K/\pi}^{K\pi}$ is due to the limited size of the simulated samples used to determine the relative efficiency for reconstructing and selecting $ B ^ \rightarrow D \pi ^ $ and $ B ^ \rightarrow D K ^ $ decays. 
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Systematic uncertainties for the branching fraction measurements, quoted as a percentage of the statistical uncertainty on the observable. 
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Statistical correlation matrix for the $ C P$ observables measured using partially reconstructed decays. 
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Statistical correlation matrix for the $ C P$ observables measured using fully reconstructed decays. 
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Systematic uncertainty correlation matrix for the $ C P$ observables measured using partially reconstructed decays. 
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Systematic uncertainty correlation matrix for the $ C P$ observables measured using fully reconstructed decays. 
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Created on 14 January 2021.