We study the resonant contributions in the process of (B) over bar (0) -> K- pi(+)mu(+)mu(-) with the K- pi(+) invariant mass square m(K pi)(2) is an element of [1, 5] GeV2. Width effects of the involved strange mesons, K*(1410), K*(0)(1430), K*(2)(1430), K*(1680), K*(3)(1780) and K*(4)(2045), are incorporated. In terms of helicity amplitudes, we derive a compact form for the full angular distributions, through which the branching ratios, forward-backward asymmetries and polarizations are attained. We propose that the uncertainties in the B -> K*(J) form factors can be pinned down by the measurements of a set of SU( 3)- related processes. Using results from the large energy limit, we derive the dependence of branching fractions on the m(K pi), and find that the K*(2) resonance has a clear signature, in particular, in the transverse polarizations.