  We study the survival probability and the first-passage time distribution for
a Brownian motion in a planar wedge with infinite absorbing edges. We
generalize existing results obtained for wedge angles of the form $\pi/n$ with
$n$ a positive integer to arbitrary angles, which in particular cover the case
of obtuse angles. We give explicit and simple expressions of the survival
probability and the first-passage time distribution in which the difference
between an arbitrary angle and a submultiple of $\pi$ is contained in three
additional terms. As an application, we obtain the short time development of
the survival probability in a wedge of arbitrary angle.
