We investigated a reversibly-propagational metamaterial perfect absorber (MPA) for X band using two separated identically-patterned copper layers, which were deposited on continuous dielectric FR-4 layers. By adjusting oblique incidence, two separated resonances are excited, then come close to each other and is finally merged to be a perfect absorption peak at 10.1 GHz. The nature of resonance is the quadrupole mode instead of the fundamental resonances in common MPAs. The mechanism of perfect absorption is the coupling of two quadrupole resonances at their superposition, leading to an enhancement of energy absorption. Finally, we numerically presented the capability of sensing thin resonant substance using the proposed MPA. The characteristic resonance of substance, which does not appear on the absorption spectrum at the limited thickness of bare substance layer, is detected with a great magnitude of signal by exploiting the absorption resonance of MPA. Our work provides another way to obtain the reversibly-propagational absorption by controlling the incident angle instead of the geometrical structure, and might be useful for the potential devices based on MPA such as detectors and sensors.