In electric power systems, a key challenge is to quickly and accurately estimate how close the system is to its stability limits. This paper investigates using synchrophasor measurements at two buses connected by a transmission line to calculate parameters for a pair of Thevenin equivalent sources, which when connected by the transmission line model provide an equivalent power system representation. As seen from the transmission line, the angle difference between the two Thevenin equivalent sources is termed the "angle across the system" for that transmission line. In the case of a lossless transmission line with voltage support on both ends, the "angle across the system" (as seen from the line) is the difference between the transmission line bus voltage phase angles; to ensure steady-state stability under these conditions, it is well known that this angle difference must be less than 90 degrees. This paper extends these ideas and proposes the notion of the "angle across the system" described above as a gauge for assessing the system's proximity to its stability limit.