Azimuthal angle (Δ) correlations are presented for a broad range of transverse momentum (0.4<pT<10 GeV/c) and centrality (0-92%) selections for charged hadrons from dijets in Au+Au collisions at sNN=200 GeV. With increasing pT, the away-side Δ distribution evolves from a broad and relatively flat shape to a concave shape, then to a convex shape. Comparisons with p+p data suggest that the away-side distribution can be divided into a partially suppressed "head" region centered at Δ~π, and an enhanced "shoulder" region centered at Δ~π±1.1. The pT spectrum for the associated hadrons in the head region softens toward central collisions. The spectral slope for the shoulder region is independent of centrality and trigger pT. The properties of the near-side distributions are also modified relative to those in p+p collisions, reflected by the broadening of the jet shape in Δ and Δη, and an enhancement of the per-trigger yield. However, these modifications seem to be limited to pT4 GeV/c, above which both the hadron pair shape and per-trigger yield become similar to p+p collisions. These observations suggest that both the away- and near-side distributions contain a jet fragmentation component which dominates for pT5 GeV/c and a medium-induced component which is important for pT4 GeV/c. We also quantify the role of jets at intermediate and low pT through the yield of jet-induced pairs in comparison with binary scaled p+p pair yield. The yield of jet-induced pairs is suppressed at high pair proxy energy (sum of the pT magnitudes of the two hadrons) and is enhanced at low pair proxy energy. The former is consistent with jet quenching; the latter is consistent with the enhancement of soft hadron pairs due to transport of lost energy to lower pT.