Strongly correlated materials often adopt electronic ground states that break rotational-symmetry of their underlying crystal structures, analogous to nematic liquid crystals. Such states are found in close proximity to and are an essential aspect of iron-based superconductors. Important questions in these materials concern the nature of their nematic and magnetic orders, whether the magnetism is due to local moments or itinerant electrons, and whether the nematic order is driven by the magnetic or the orbital degree of freedom. Using scattering techniques we demonstrate the presence of intertwined nematic and stripe-type magnetic orders in semiconducting KFe0.8Ag1.2Te2, a structural analogue of iron-based superconductors. A small strain induces sizeable magnetic anisotropy above the magnetic and nematic transition temperatures, indicating a large nematic susceptibility while realizing a strain-induced spin-nematic state. Because KFe0.8Ag1.2Te2 is a semiconductor devoid of a Fermi surface, its magnetic and nematic orders likely arise from interactions between local moments. Such interactions should be important for systems containing Fe-pnitogen/chalcogen planes in general, including iron-based superconductors. Our results suggest several aspects of the phenomenology of iron-based superconductor result from the unique geometry of the iron-pnictogen/chalcogen planes.