Nodal angle-resolved photoemission spectra taken on overdoped La1.77Sr0.23CuO4 are presented and analyzed. It is proven that the low-energy excitations are true Landau Fermi-liquid quasiparticles. We show that momentum and energy distribution curves can be analyzed self-consistently without quantitative knowledge of the bare band dispersion. Finally, by imposing Kramers-Kronig consistency on the self-energy Sigma, insight into the quasiparticle residue is gained. We conclude by comparing our results to quasiparticle properties extracted from thermodynamic, magnetoresistance, and high-field quantum oscillation experiments on overdoped Tl2Ba2CuO6+delta.