[摘要]:We report a study of B -> (J/psi gamma)K and B -> (psi'gamma)K decay modes using 772 X 10(6) B (B) over bar events collected at the Y(4S) resonance with the Belle detector at the KEKB energy-asymmetric e(+)e(-) collider. We observe X(3872) -> J/psi gamma and report the first evidence for chi(c2) -> J/psi gamma in B -> (X(c (c) over bar)gamma)K decays, while in a search for X(3872) -> psi'gamma no significant signal is found. We measure the branching fractions, B(B(+/-) -> X(3872)K(+/-))B(X(3872) -> J/psi gamma) = (1.78(-0.44)(+0.48) +/- 0.12) X 10(-6), B(B(+/-) -> chi(c2)K(+/-)) = (1.11(-0.34)(+0.36) +/- 0.09) X 10(-5), B(B(+) -> X(3872)K(+))B(X(3872) -> psi'gamma) < 3.45 X 10(-6) (upper limit at 90% C. L.), and also provide upper limits for other searches.