  Cabibbo-allowed charmed meson decays into a pseudoscalar meson and an
axial-vector meson are studied. The charm to axial-vector meson transition form
factors are evaluated in the Isgur-Scora-Grinstein-Wise quark model. The dipole
momentum dependence of the $D\to K$ transition form factor and the presence of
a sizable long-distance $W$-exchange are the two key ingredients for
understanding the data of $D\to \bar Ka_1$. The $K_{1A}-K_{1B}$ mixing angle of
the strange axial-vector mesons is found to be $\approx \pm37^\circ$ or
$\pm58^\circ$ from $\tau\to K_1\nu_\tau$ decays. The study of $D\to
K_1(1270)\pi, K_1(1400)\pi$ decays excludes the positive mixing-angle
solutions. It is pointed out that an observation of the decay $D^0\to
K_1^-(1400)\pi^+$ at the level of $5\times 10^{-4}$ will rule out
$\theta\approx -37^\circ$ and favor the solution $\theta\approx -58^\circ$.
Though the decays $D^0\to \bar K_1^0\pi^0$ are color suppressed, they are
comparable to and even larger than the color-allowed counterparts: $\bar
K_1^0(1270)\pi^0\sim K_1^-(1270)\pi^+$ and $\bar K_1^0(1400)\pi^0>
K_1^-(1400)\pi^+$. The finite width effect of the axial-vector resonance is
examined. It becomes important for $a_1(1260)$ in particular when its width is
near 600 MeV.
