  The Milky Way disk exhibits intricate orbit substructure of still-debated
dynamical origin. The angle variables $(\theta_\phi,\theta_R)$ -- which are
conjugates to the actions $(L_z,J_R)$, and describe a star's location along its
orbit -- are a powerful diagnostic to identify $l$:$m$ resonances via the orbit
shape relation $\Delta \theta_R / \Delta \theta_\phi = -m/l$. In the past,
angle signatures have been hidden by survey selection effects (SEs). Using test
particle simulations of a barred galaxy, we demonstrate that \emph{Gaia} should
allow us to identify the Galactic bar's Outer Lindblad Resonance ($l=+1, m=2$,
OLR) in angle space. We investigate strategies to overcome SEs. In the angle
data of the \emph{Gaia} DR2 RVS sample, we independently identify four
candidates for the OLR and therefore for the pattern speed $\Omega_\text{bar}$.
The strongest candidate, $\Omega_\text{bar}\sim1.4\Omega_0$, positions the OLR
above the `Sirius' moving group, agrees with measurements from the Galactic
center, and might be supported by higher-order resonances around the
`Hercules/Horn'. But it misses the classic orbit orientation flip, as discussed
in the companion study on actions. The candidate
$\Omega_\text{bar}\sim1.2\Omega_0$ was also suggested by the action-based
study, has the OLR at the `Hat', is consistent with \emph{slow bar} models, but
still affected by SEs. Weaker candidates are $\Omega_\text{bar}=1.6\Omega_0$
and $1.74\Omega_0$. In addition, we show that the stellar angles do not support
the `Hercules/Horn' being created by the OLR of a \emph{fast bar}. We conclude
that -- to resolve if `Sirius' or `Hat' is related to the bar's OLR -- more
complex dynamical explanations and more extended data with well-behaved SEs are
required.
