The Large Hadron Collider (LHC) is currently the world's premier facility for the study of high-energy particle physics. The goal of the Compact Muon Solenoid (CMS) experiment at the LHC is to search for new phenomena in particle physics at the TeV scale. One of the mysteries that data from CMS may solve is the origin of dark matter. It is hoped that dark matter particles will be produced in the proton-proton collisions of the LHC, either by themselves or along with other new particles. This would allow the laws that govern dark matter to be explored. Collisions containing dark matter particles will pose new challenges for collider physics, necessitating the development of new methods to deal with these problems. One class of methods for addressing these problems is kinematic endpoint variables such as MT2 and MCT. A great deal of theoretical work has been done in developing these methods, but they have seldom been applied in experiment. We apply these methods to data taken with CMS to address two problems: mass measurement in underconstrained events and searches for new physics. In doing so, we also provide a new measurement of the top-quark mass and search for new physics in events with two leptons and a momentum imbalance.