English: We present measurements of azimuthal correlations of charged hadron pairs in √sNN=200 GeV Au+Au collisions for the trigger and associated particle transverse-momentum ranges of 1<ptT<10GeV/c and 0.5<paT<10GeV/c. After subtraction of an underlying event using a model that includes higher-order azimuthal anisotropy v2, v3, and v4, the away-side yield of the highest trigger-pT(ptT>4GeV/c) correlations is suppressed compared with that of correlations measured in p+p collisions. At the lowest associated particle pT(0.5<paT<1GeV/c), the away-side shape and yield are modified relative to those in p+p collisions. These observations are consistent with the scenario of radiative-jet energy loss. For the low-pT trigger correlations (2<ptT<4GeV/c), a finite away-side yield exists and we explore the dependence of the shape of the away-side within the context of an underlying-event model. Correlations are also studied differentially versus event-plane angle Ψ2 and Ψ3. The angular correlations show an asymmetry when selecting the sign of the difference between the trigger-particle azimuthal angle and the Ψ2 event plane. This asymmetry and the measured suppression of the pair yield out-of-plane is consistent with a path-length-dependent energy loss. No Ψ3 dependence can be resolved within experimental uncertainties.