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The ALICE Collaboration reports measurements of the semi-inclusive distribution of charged-particle jets recoiling from a high transverse momentum (high$p_{\mathrm{T}}$) charged hadron, in$pp$and central Pb-Pb collisions at center-of-mass energy per nucleon–nucleon collision$\sqrt{s_{\mathrm{NN}}}=5.02$TeV. The large uncorrelated background in central Pb-Pb collisions is corrected using a data-driven statistical approach which enables precise measurement of recoil jet distributions over a broad range in$p_{\mathrm{T},\mathrm{ch}\mathrm{jet}}$and jet resolution parameter$R$. Recoil jet yields are reported for$R=0.2$, 0.4, and 0.5 in the range$7<p_{\mathrm{T},\mathrm{ch}\mathrm{jet}}<140 \mathrm{GeV}/c$and$\pi /2<\mathrm{\Delta }\phi <\pi$, where$\mathrm{\Delta }\phi$is the azimuthal angular separation between hadron trigger and recoil jet. The low-$p_{\mathrm{T},\mathrm{ch}\mathrm{jet}}$reach of the measurement explores unique phase space for studying jet quenching, the interaction of jets with the quark–gluon plasma generated in high-energy nuclear collisions. Comparison of$p_{\mathrm{T},\mathrm{ch}\mathrm{jet}}$distributions from$pp$and central Pb-Pb collisions probes medium-induced jet energy loss and intra-jet broadening, while comparison of their acoplanarity distributions explores in-medium jet scattering and medium response. The measurements are compared to theoretical calculations incorporating jet quenching.