  The electromagnetic transitions of $^9$Be with linearly polarized
$\gamma$-rays are calculated by using the $\alpha$~+~$\alpha$~+~$n$ three-body
model and the complex-scaled solutions of the Lippmann-Schwinger equation; the
azimuthal angle distributions of the emitted neutrons are investigated. We
calculate the anisotropy parameter as a function of the photon incident energy
$E_\gamma$, and discuss how sensitive the anisotropy parameter is to nuclear
structure and transition modes. The result suggests that the azimuthal angle
distribution of neutrons emitted from the $^9$Be($\gamma$,$n$) reaction with
the linearly polarized $\gamma$-rays is useful to identify the resonances in
the final states even if it is not clearly observed in the cross section.
