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.
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