We report the observation of a nontrivial spin texture in Dirac node arcs, i.e., novel topological objects formed when Dirac cones of massless particles extend along an open one-dimensional line in momentum space. We find that such states are present in all the compounds of the tetradymite M_{2}Te_{2}X family (M=Ti, Zr, or Hf and X=P or As) regardless of the weak or strong character of the topological invariant. The Dirac node arcs in tetradymites are thus the simplest possible textbook example of a type-I Dirac system with a single spin-polarized node arc.