  Angularities are event shapes whose sensitivity to the splitting angle of a
collinear emission is controlled by a continuous parameter $b$, with $ -1 < b <
\infty$. When measured with respect to the thrust axis, this class of QCD
observables includes thrust ($b=1$) and jet broadening ($b=0$), the former
being insensitive to the recoil of soft against collinear radiation, while the
latter being maximally sensitive to it. Presently available analytic results
for angularity distributions with $b \neq 0$ can be applied only close to the
thrust limit since recoil effects have so far been neglected. As a first step
to establish a comprehensive theoretical framework based on Soft-Collinear
Effective Theory valid for all recoil-sensitive angularities, we compute for
the first time angularity distributions at one-loop order in $\alpha_s$ for all
values of $b$ taking into account recoil effects. In the differential cross
section, these amount to novel sub-leading singular contributions and/or power
corrections, where the former are characterized by fractional powers of the
angularity and contribute appreciably close to the peak region, also for $b
\gtrsim 0.5$. Our calculations are checked against various limits known in the
literature and agree with the numerical output of the Event2 generator.
