A consideration of ultra-thin resonant absorbers of electromagnetic radiation utilizing high-impedance metasurfaces is carried out in terms of an equivalent circuit theory. By incorporating a thin layer of tunable dielectric into such structures it is feasible to manipulate the radiation amplitude and phase under the condition of a small thickness of the dielectric layer in comparison with the radiation wavelength. As such a dielectric, the nematic liquid crystal 5CB with a thickness of 80 um was chosen, and a 5CB-based prototype of an absorbing metastructure of the reflective type optimized for operation in the vicinity of a frequency of 140 GHz was fabricated and experimentally studied. Testing the structure revealed good agreement between the calculated and experimental reflection spectra. The results of this work can be useful for modeling and developing quasi-optical and integrated active devices of terahertz photonics.