  In a strong gravitational lens, perturbations by low-mass dark matter halos
can be detected by differences between the measured image fluxes relative to
the expectation from a smooth model for the mass distribution which contains
only the gravitational effects of the main deflector. The abundance of these
low-mass structures can be used to constrain the properties of dark matter.
Traditionally only the lensed quasar positions have been to predict the
smooth-model flux ratios. We demonstrate that significant additional
information can be gained by using the lensed quasar host galaxy which appears
as an extended arc and constrains the smooth-model over a much larger angular
area. We simulate Hubble Space Telescope-quality mock observations based on the
lensing system WGD2038-4008 and we compare the model-predicted flux ratio
precision and accuracy for two cases; one of which the inference is based only
on the lensed quasar image positions, and the other based on the extended arcs
as well as lensed quasar image positions. For our mock lens systems we include
both elliptical, and higher order m=3 and m=4 multipole terms in the
smooth-mass distributions with amplitudes based on the optically measured
shapes of massive elliptical galaxies. We find that the extended arcs improve
the precision of the model-predicted flux ratios by a factor of 6-8, depending
on the strength of the multipole terms. Furthermore, with the extended arcs, we
are also able to accurately recover the m=3, 4 mass multipole strengths and
angles $a_3/a$, $a_4/a$, $\phi_3-\phi_0$, and $\phi_4-\phi_0$ to a precision of
0.002, 0.002, $3^\circ$ and $3^\circ$, respectively. This work implies that
lensed arcs can constrain deviations from ellipticity in strong lens systems,
and potentially lead to more robust constraints on substructure properties from
flux ratios.
