  Parton energy loss has been established as an essential signature of the
Quark-Gluon Plasma (QGP) in heavy ion collisions since the earliest
measurements at RHIC indicating suppression of hadron spectra at high
$p_{\rm{T}}$ and coincidence yields. Understanding this phenomenon of jet
quenching is a requirement for extracting the microscopic properties of the QGP
via jet-tomography. STAR has recently introduced a technique called Jet
Geometry Engineering (JGE) wherein we enforce particular selection criteria
imposed on the jet collection, such as recoiling off a high $p_{\rm{T}}$ hadron
trigger along with an additional transverse momentum threshold for jet
constituents in events with back-to-back di-jets. With JGE, we are able to
control the extent of energy loss ranging from quenched/imbalanced to
recovered/balanced di-jets. Since jet quenching is also expected to be
dependent on the resolution/transverse-length scales with which the jet probes
the medium, it is necessary to perform differential measurements with a handle
on both momentum and angular scales. To quantify the angular scale within jets,
we present the first measurement of the jet's inherent angular structure in
Au$+$Au collisions at $\sqrt{s_{\mathrm{NN}}} = $ 200 GeV via the opening angle
between the two leading sub-jets ($\theta_{\rm{SJ}}$). We also measure the
di-jet asymmetry $A_{\rm{J}}$ differentially as a function of the
$\theta_{\rm{SJ}}$ observable for these di-jets and find no significant
dependence of the energy loss on the opening angle of the recoil jet.
