STAR measurements of dihadron azimuthal correlations ($\Delta\phi$) are reported in mid-central (20-60\%) Au+Au collisions at $\sqrt{s_{_{\rm NN}}}=200$ GeV as a function of the trigger particle's azimuthal angle relative to the event plane, $\phi_{s}=|\phi_{t}-\psi_{\rm EP}|$. The elliptic ($v_2$), triangular ($v_3$), and quadratic ($v_4$) flow harmonic backgrounds are subtracted using the Zero Yield At Minimum (ZYAM) method. The results are compared to minimum-bias d+Au collisions. It is found that a finite near-side ($|\Delta\phi|<\pi/2$) long-range pseudorapidity correlation (ridge) is present in the in-plane direction ($\phi_{s}\sim 0$). The away-side ($|\Delta\phi|>\pi/2$) correlation shows a modification from d+Au data, varying with $\phi_{s}$. The modification may be a consequence of pathlength-dependent jet-quenching and may lead to a better understanding of high-density QCD.