We have investigated the doping and temperature dependences of the pseudogap and superconducting gap in the single-layer cuprate La2-xSrxCuO4 by angle-resolved photoemission spectroscopy. The results clearly exhibit two distinct energy and temperature scales, namely, the gap around (pi, 0) of magnitude Delta* and the gap around the node characterized by the d-wave order parameter Delta0. In comparison with Bi2212 having higher Tc's, Delta0 is smaller, while Delta* and T* are similar. This result suggests that Delta* and T* are approximately material-independent properties of a single CuO2 plane, in contrast to the material-dependent Delta0, representing the pairing strength.