  We report magnetic torque measurements on iron-pnictide superconductors
Ba$_{1-x}$K$_x$Fe$_2$As$_2$ ($x \approx$ 0.69 and 0.76) up to an applied field
of $B_a$ = 45 T. The peak effect is observed in torque-vs-field curves below
the irreversibility field. It is enhanced and becomes asymmetric as the field
is tilted from the $c$ axis. For field directions close to the $ab$ plane,
increasing- and decreasing-field curves peak at markedly different fields, and
exhibit a sharp jump, suggestive of a first-order phase transition, on the
high- and the low-field side of the peak, respectively. Complicated history
dependence of the torque is observed in the peak-effect region. We construct
and discuss the temperature ($T$)--applied-magnetic-field ($B_a$) phase
diagram. Since the upper critical field for the $ab$-plane direction is
comparable to the Pauli limit, we also consider possible influence of the spin
paramagnetic effect on the anomalous peak effect.
