  Various phenomenological studies indicate that the mixing angle
$\theta_{K_1}$ of $K_{1A}$ and $K_{1B}$, the strange partners of the
axial-vector mesons $a_1(1260)$ and $b_1(1235)$, respectively, lies in the
vicinity of $35^\circ$ or $55^\circ$, but whether this angle is larger or
smaller than $45^\circ$ still remains controversial. When the
$f_1(1285)$-$f_1(1420)$ mixing angle $\theta_{^3P_1}$ and the
$h_1(1170)$-$h_1(1380)$ mixing angle $\theta_{^1P_1}$ are determined from the
mass relations, they depend on the masses of $K_{1A}$ and $K_{1B}$, which in
turn depend on the mixing angle $\theta_{K_1}$. We show that the approximate
decoupling of the light $q\bar q$ state from the heavier $s \bar s$ state,
which is empirically valid for vector, tensor and $3^{--}$ mesons, when applied
to isoscalar axial-vector mesons, will enable us to discriminate different
solutions of $\theta_{^3P_1}$ and $\theta_{^1P_1}$ and pick up
$\theta_{K_1}\sim 35^\circ$. Indeed, for $\theta_{K_1}\sim 55^\circ$, the
predicted $\theta_{^1P_1}$ disagrees sharply with the recent lattice
calculation and the implied large $s\bar s$ content of $h_1(1170)$ and $q\bar
q$ component of $h_1(1380)$ cannot explain the observation of their strong
decays. We conclude that $\theta_{K_1}$ is smaller than $45^\circ$.
