Line tension plays several important roles in lipid monolayers such as influencing the morphology of two-phase domains and, in biological systems, mediating protein-lipid interactions. Despite this, no widely applicable technique exists for measuring the line tension in liquid-condensed-liquid-expanded (LC-LE) phase monolayers common in lung surfactant and tear films, among other systems. We develop a non-perturbative, broadly applicable technique for measuring the line tension in LC-LE monolayers using two-dimensional Mullins-Sekerka theory. Our measured line tensions are consistent with theoretical predictions and decrease with increasing cholesterol fraction, providing a quantitative effect to cholesterol’s “line-active” nature in LC-LE monolayers. An understanding of MS theory in 2D monolayers can also be used broadly to explain and rationalize the morphologies observed in many other systems. Additionally, this technique provides a way for decoupling the dipole density difference from line tension measurements in many equilibrium theories, allowing us to provide what we believe to be the first non-theoretical measurement of dipole density difference in LC-LE monolayers.