We have analysed the emission-line properties of 6019 Type II active galactic nuclei (AGNs) at redshifts in the range 0.4–0.8 with [O III] luminosities greater than 3×108L⊙, characteristic of the Type II quasars first identified in population studies by Zakamska et al. The AGNs are drawn from the CMASS sample of galaxies with stellar masses greater than 1011M⊙ that were studied as part of the Baryon Oscillation Spectroscopic Survey (BOSS) and comprise 0.5 per cent of the total population of these galaxies. Individual spectra have low S/N, so the analysis is carried out on stacked spectra in bins of [O III] luminosity and estimated stellar age. The emission line ratios of the stacks are well fit with simple uniform-density photoionization models with metallicities between solar and twice solar. In the stacks, a number of emission lines are found to have distinct broad components requiring a double Gaussian rather than a single Gaussian fit, indicative of outflowing ionized gas. These are: [O III] λ4959, [O III] λ5007, [O II] λ3727,3729, and H αλ6563. Higher ionization lines such as [Ne III] λ3869 and [Ne V] λ3345 are detected in the stacks, but are well fit by single Gaussians. The broad components typically contain a third of the total line flux and have widths of 600 km s−1 for the oxygen lines and 900 km s−1 for H α. The fraction of the flux in the broad component and its width are independent of [O III] luminosity, stellar age, radio, and mid-IR luminosity. The stellar mass of the galaxy is the only parameter we could identify that influences the width of the broad line component.