We perform a thermodynamic analysis of various contributions to the size dependence of the contact-angle cosine for both axisymmetric and cylindrical sessile droplets. This shows that a commonly used method to determine the line tension from the slope of the contact-angle cosine dependence on the three-phase contact-line curvature (for axisymmetric droplets) provides a certain combination of the line tension, the adsorptions at the three interfaces, and the macroscopic contact angle. To extract the contribution related to the contact line in the leading order and determine the line tension, we propose a simple technique using droplet-size dependences of the contact angle for axisymmetric and cylindrical droplets under the same conditions.