  We report the first detailed investigation of K$_2$MnS$_2$ and K$_2$MnSe$_2$
from the K$_2$MnS$_2$ structure type and their magnetic solid solution
K$_2$MnS$_{2-x}$Se$_x$ and find that compounds of this structure type consist
of strongly-coupled pseudo-one-dimensional antiferromagnetic chains that
collectively represent a frustrated two-dimensional triangular antiferromagnet.
Bulk samples of K$_2$MnS$_{2-x}$Se$_x$ with $0 \leq x \leq 2$ are characterized
using X-ray diffraction, neutron diffraction, magnetization and heat capacity
measurements. An incommensurate cycloid magnetic structure with a magnetic
propagation vector $k = [0.58~0~1]$ is observed for all samples in
K$_2$MnS$_{2-x}$Se$_x$, and the ordering is robust despite a 12\% increase in
cell volume. Geometric frustration of chains results in incommensurability
along $a$ and a two-step magnetic transition. The varying geometries accessible
in compounds of this structure type are presented as promising avenues to tune
frustration.
