The effects of cosolvents on the microstructure of the lyotropic Liquid crystals formed by poly(ethylene oxide)-poly(propylene oxide)-poly(ethylene oxide) (PEO-PPO-PEO) triblock: copolymers in water were examined in ternary isothermal systems consisting of a representative PEO-PPO-PEO copolymer (Pluronic P105, (EO)(37)(PO)(58)(EO)(37)), water, and a polar cosolvent (glycerol; propylene glycol, ethanol, or glucose, referred to as "glycols"). The characteristic length scales of the lyotropic liquid crystals were established using small-angle X-ray scattering (SAXS). The SAXS data are analyzed and discussed with respect to (i) influence of the different glycols and the glycol content on the characteristic length scales, (ii) area occupied by one macromolecule at the polar/apolar interface, (iii) location of the different; glycols in the microstructure, and (iv) glycol ability to modify the interfacial curvature through swelling the PEO-PPO-PEO macromolecule to different extents. The trends in the glycol effects observed in the ternary phase diagrams ("macroscopic" information) are confirmed and reinforced by the detailed microstructural information obtained here by SAXS. A correlation is found between the glycol effect on the microstructure of the lyotropic liquid crystals (the degree of relative swelling) and the glycol polarity (expressed in terms of octanol/water partition coefficient, dielectric constant or solubility parameter).