Final answer:
Astronomers discovered the universe is expanding through measurements of the redshifts of galaxies and the study of galaxy spectra.
Step-by-step explanation:
The observational evidence that led astronomers to discover that the universe is expanding includes measurements of the redshifts of galaxies and the study of the spectra of galaxies.
Edwin Hubble's observations in 1929 showed that galaxies farther away from us have a larger redshift, indicating that they are moving away at a faster rate. This provided evidence for the expanding universe.
Additionally, the abundance of deuterium, helium, and lithium in nearby stars and galaxies, as well as measurements of the motions of stars in galaxies and the rate of expansion of the universe, helped confirm the expansion.