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A measurement of the angular structure of inclusive jets and those containing a prompt D0 meson in proton-proton collisions at the LHC at a center-of-mass energy of 5.02 TeV is presented. The data corresponding to an integrated luminosity of 301 pb−1 were collected by the CMS experiment in 2017. Two jet grooming algorithms, late-kT and soft drop, are used to study the intrajet radiation pattern using iterative Cambridge-Aachen declustering. The splitting-angle distributions of jets with transverse momentum (pT) of around 100 GeV, obtained with these two algorithms, show that there is a shift of the distribution for jets containing a prompt D0 meson with respect to inclusive jets. The suppression of emissions at small angles observed in the late-kT grooming approach is consistent with the dead-cone effect, whereas the similar suppression for splittings selected with the soft-drop algorithm appears to be induced by gluon splitting to charm quark-antiquark pairs at large angles. The measured distributions are corrected to the particle level and can be used to constrain model predictions for the substructure of high-pT charm quark jets.