We present a photometric and spectroscopic study of stellar populations in the X-ray-luminous cluster of galaxies RXJ0142.0+2131 at z=0.280. This paper analyses the results of high signal-to-noise spectroscopy, as well as g-, r-, and i-band imaging, using the Gemini Multi-Object Spectrograph on Gemini North. Of 43 spectroscopic targets, we find 30 cluster members over a range in color. Central velocity dispersions and absorption-line strengths for lines in the range 3700A < lambda_rest < 5800A are derived for cluster members, and are compared with a low-redshift sample of cluster galaxies, and single stellar population (SSP) models. We use a combination of these indicators to estimate luminosity-weighted mean ages, metallicities ([M/H]), and alpha-element abundance ratios ([alpha/Fe]). RXJ0142.0+2131 is a relatively poor cluster and lacks galaxies with high central velocity dispersions. Although the red sequence and the Faber-Jackson relation are consistent with pure passive evolution of the early-type population with a formation redshift of z_form = 2, the strengths of the 4000A break and scaling relations between metal line indices and velocity dispersion reject this model with high significance. By inverting SSP models for the Hbeta_G, Mgb, and <Fe> line indices, we calculate that, at a given velocity dispersion and metallicity, galaxies in RXJ0142.0+2131 have luminosity-weighted mean ages 0.14 +- 0.07 dex older than the low-redshift sample. We also find that [alpha/Fe] in stellar populations in RXJ0142.0+2131 is 0.14 +- 0.03 greater than at low redshift. All scaling relations are consistent with these estimated offsets. (abridged)
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