A vane arc segment includes ceramic matrix composite (CMC) fairing that has an airfoil section, a first single-sided platform at the outer radial end projecting from the suction side wall, and a second single-sided platform at the inner radial end projecting from the pressure side wall. The first single-sided platform is comprised of a fiber layer that extends from the airfoil section and turns into the first single-sided platform, and the second single-sided platform is comprised of the fiber layer that from the airfoil section and turns into the second single-sided platform.