To solve the problem of finding the unknown mass on one side of a balance, the key concept is torque. The moments on both sides of the balance must be equal for the system to be in equilibrium. The known variables include the mass of the object on the opposite side, the angle of the balance, and the distances from the fulcrum. The angle does not affect the torque calculation as long as the fulcrum point remains consistent. Understanding these principles will aid in accurately determining the unknown mass.