  The 2-point angular correlation function $w(\theta)$ (2PACF), where $\theta$
is the angular separation between pairs of galaxies, provides the transversal
Baryon Acoustic Oscillation (BAO) signal almost model-independently. In this
paper we use 409,337 luminous red galaxies in the redshift range $z =
[0.440,0.555]$ obtained from the tenth data release of the Sloan Digital Sky
Survey (SDSS DR10) to estimate $\theta_{\rm{BAO}}(z)$ from the 2PACF at six
redshift {shells}. Since noise and systematics can hide the BAO signature in
the $w - \theta$ plane, we also discuss some criteria to localize the acoustic
bump. We identify two sources of model-dependence in the analysis, namely, the
value of the acoustic scale from Cosmic Microwave Background (CMB) measurements
and the correction in the $\theta_{\rm{BAO}}(z)$ position due to projection
effects. Constraints on the dark energy equation-of-state parameter w$(z)$ from
the $\theta_{\rm{BAO}}(z)$ diagram are derived, as well as from a joint
analysis with current CMB measurements. We find that the standard $\Lambda$CDM
model as well as some of its extensions are in good agreement with these
$\theta_{\rm{BAO}}(z)$ measurements.
