  We study the effects of electroweak penguin (EWP) amplitudes in $B$ meson
decays into two charmless pseudoscalars in the approximation of retaining only
the dominant EWP operators $Q_9$ and $Q_{10}$. Using flavor SU(3) symmetry, we
derive a set of model-independent relations between EWP contributions and
tree-level decay amplitudes one of which was noted recently by Neubert and
Rosner. Two new applications of these relations are demonstrated in which
uncertainties due to EWP corrections are eliminated in order to determine a
weak phase. Whereas the weak angle $\alpha$ can be obtained from $B\to\pi\pi$
free of hadronic uncertainties, a determination of $\gamma$ from $B^{0,\pm}\to
K\pi^{\pm}$ requires the knowledge of a ratio of certain tree-level hadronic
matrix elements. The smallness of this ratio implies a useful constraint on
$\gamma$ if rescattering can be neglected.
