The angular dependence of jet suppression encodes key information about the process of energy and momentum hydrodynamization, and for this reason can be used to greatly improve our understanding of fundamental aspects of the jet/QGP interaction. In this work we study jet suppression from small to very large radius, for low and very high energy jets at the LHC and RHIC. We use the hybrid strong/weak coupling model for jet quenching that combines perturbative shower evolution with an effective strongly coupled description of the energy and momentum transfer from the jet into the QGP. Because of energy-momentum conservation, the wake created by the jet enhances or depletes the yield of particles generated at the freeze-out hypersurface depending on their orientation with respect to the direction of the jet. We find that jet suppression is remarkably independent of the anti-$k_T$ radius R, specially at LHC, first slightly increasing by opening R, then at larger values of R slowly decreasing. This nearly independence of jet suppression with R arises from two competing effects, namely the larger energy loss of the energetic jet components, which tends to increase suppression, against the partial recovery of the lost energy due to medium response, which reduces suppression. We find that the boosted medium from the recoiling jet depletes the amount of QGP in the direction opposite to it in the transverse plane, inducing energy loss due to an over-subtraction effect. We show that this unique signature of the hydrodynamization of part of the jet energy can be scrutinized by selecting samples of dijet configurations with different relative rapidities between the leading and the subleading jet.