  We perform a comprehensive analysis of medium modifications on ungroomed jet
angularities, $\tau_a$, within the framework of Soft-Collinear Effective Theory
with Glauber gluons (SCET$_{\rm G}$). Angularities are a one-parameter family
of jet substructure observables with angularity exponent $a<2$ for infrared
safety. Variation of the angularity exponent allows to modify the relative
weighting of the collinear-to-soft radiations in the jet. In this article, we
focus on angularity exponents $a<1$ and provide detailed results for $a=-1,0$,
and $0.5$. Within SCET$_{\rm G}$, the interaction between jet and medium
constituents is comprehended by off-shell Glauber gluons generated from the
color gauge fields in the medium. While the medium modifications are
incorporated in the jet function via the use of in-medium splitting functions,
the soft function remains unmodified for $a<1$. For all values of $a$, we find
that in the medium, the distributions are narrower and have a steeper fall
compared to the vacuum ones. This redistribution of the ungroomed angularity
spectrum is more apparent for a jet with a larger cone size. We also present
results for the medium sensitivity towards $p_T$ of the jet and for a jet
initiated in a less central event ($10-30\%$ centrality). Finally, we provide
the ratios of nucleus-nucleus and proton-proton differential angularity
distributions for different angularity exponents and for two values of the jet
radius parameter.
