  We study the $\rho$ and $\omega$ meson contribution to the radiative decays
$X(3872)\rightarrow J/\psi \pi \gamma$ and $X(3872)\rightarrow J/\psi \pi\pi
\gamma$. The $X(3872)\rightarrow J/\psi \pi \gamma$ is dominated by the
$\omega$ meson. As for the $X(3872)\rightarrow J/\psi \pi\pi \gamma$, the
contributions of the cascade decays through the $\rho$ and $\omega$ mesons are
strongly suppressed with respect to the diagrams which proceed either through
the $\psi(2S)$ or the three body decay of $\rho$. The branching ratios of
$X(3872)\rightarrow J/\psi \pi \gamma$ and $X(3872)\rightarrow J/\psi \pi\pi
\gamma$ are $(8.10^{+3.50}_{-2.88})\times10^{-3}$ and $(2.38\pm1.06)\%$, which
may be accessible by the BESIII and LHCb Collaborations. Especailly, the
$X(3872)\rightarrow J/\psi \pi \gamma$ and $X(3872)\rightarrow J/\psi
\pi^+\pi^- \gamma$ decays can be employed to extract the couplings
$g_{X\psi\omega}$ and $g_{X\psi\rho}$, which probe the isoscalar and isovector
components of the X(3872) wave function respectively.
