  We discuss a simple approach to measure the weak mixing angles phi_s and
phi_d of the Bs and Bd systems in the presence of New Physics. We present a new
expression that allows one to measure directly the New Physics mixing angles if
New Physics contributes significantly to the mixing only. We apply the method
to specific penguin-mediated B->PP, B->PV and B ->VV modes. We provide a very
stringent and simple bound on the direct CP asymmetries of all these modes, the
violation of which is a signal of New Physics in decay. Within the same
theoretical framework, an updated prediction for the branching ratio of Bs->K0*
anti-K0* is presented, which can be compared with a recent LHCb analysis.
