Detecting the magnetic states of synthetic antiferromagnets (SAFs) at the nanoscale is challenging due to their low net magnetization. We demonstrate an electrical method based on tunneling magnetoresistance (TMR) in nanoscale magnetic tunnel junctions to selectively detect the magnetization of a single SAF sublayer. TMR hysteresis loops reveal distinct switching behaviors governed by the competition between magnetic anisotropy and interlayer exchange coupling. This sensitivity enables direct quantification of exchange coupling under both field- and spin-transfer torque-driven reversals, while accessing the overall SAF magnetic state independent of its net magnetization.