Nonstoichiometric NaxCoO2 (0.5 < x < 1) consists of CoO2 layers made up of edge-sharing CoO6 octahedra and exhibits strongly anisotropic magnetic susceptibilities as well as metallic properties. A modified Curie-Weiss law was proposed for systems containing anisotropic magnetic ions to analyze the magnetic susceptibilities of NaxCoO2 (x approximate to 0.75), and implications of this analysis were explored. Our study shows that the low-spin Co4+ (S = 1/2) ions of NaxCoO2 generated by the Na vacancies cause the anisotropic magnetic properties of NaxCoO2 and suggests that the six nearest-neighbor Co3+ ions of each Co4+ ion adopt the intermediate-spin electron configuration, thereby behaving magnetically like low-spin Co4+ ions. The Weiss temperature of NaxCoO2 is more negative along the direction of the lower g factor (i.e., theta(parallel to) < theta(perpendicular to) < 0 and g(parallel to) < g(perpendicular to)). The occurrence of intermediate-spin Co3+ ions surrounding each Co4+ ion accounts for the apparently puzzling magnetic properties of NaxCoO2 (x approximate to 0.75), i.e., the large negative Weiss temperature, the three-dimensional antiferromagnetic ordering below similar to 22 K, and the metallic properties. The picture of the magnetic structure derived from neutron scattering studies below similar to 22 K is in apparent conflict with that deduced from magnetic susceptibility measurements between similar to 50 and 300 K. These conflicting pictures are resolved by noting that the spin exchange between Co3+ ions is more strongly antiferromagnetic than that between Co4+ and Co3+ ions.