  Relativistic magnetohydrodynamic shocks are efficient particle accelerators,
often invoked in the models of gamma-ray bursts (GRBs) and shock-powered fast
radio bursts (FRBs). Most theoretical studies assume a perpendicular shock with
an ordered magnetic field perpendicular to the shock normal. However, the
degree of magnetization $\sigma$ and the magnetic field geometry in
shock-powered GRB/FRB scenarios are still poorly constrained by observations.
Analogous to the magnetization $\sigma$ associated with the total field
strength, we define a tangential magnetization $\sigma_\perp$ associated with
the tangential field component. We explore the jump conditions of magnetized
relativistic shocks, either with an ordered field of arbitrary inclination
angle or with a random field of arbitrary anisotropy. In either case, we find
that the jump conditions of relativistic shocks are governed by the tangential
magnetization $\sigma_\perp$ instead of the total magnetization $\sigma$,
insensitive to the inclination angles or the anisotropy of the pre-shock
magnetic field. The approximated analytical solution developed in this work
could serve as a quick check for numerical simulations and apply to theoretical
studies of GRBs/FRBs with a more general field geometry.
