  We present measurements of azimuthal correlations of charged hadron pairs in
$\sqrt{s_{_{NN}}}=200$ GeV Au$+$Au collisions for the trigger and associated
particle transverse-momentum ranges of $1<p_T^t<10$~GeV/$c$ and
$0.5<p_T^a<10$~GeV/$c$. After subtraction of an underlying event using a model
that includes higher-order azimuthal anisotropy $v_2$, $v_3$, and $v_4$, the
away-side yield of the highest trigger-\pt ($p_T^t>4$~GeV/$c$) correlations is
suppressed compared to that of correlations measured in $p$$+$$p$ collisions.
At the lowest associated particle $p_T$ ($0.5<p_T^a<1$ GeV/$c$), 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-$p_T$ trigger correlations ($2<p_T^t<4$ GeV/$c$), 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 $\Psi_2$ and $\Psi_3$. The angular
correlations show an asymmetry when selecting the sign of the difference
between the trigger-particle azimuthal angle and the $\Psi_2$ 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 $\Psi_3$ dependence can
be resolved within experimental uncertainties.
