Final answer:
Astronomers determined that the Milky Way Galaxy is spiral-shaped by analyzing its rotational motion.
Step-by-step explanation:
Astronomers determined that the Milky Way Galaxy is spiral-shaped by detecting its rotational motion. They measured the rotation speed of stars or gas in spiral galaxies by observing the Doppler effect. The faster something is moving toward or away from us, the greater the shift of the lines in its spectrum. By analyzing this shift, astronomers were able to determine the spiral shape of the Milky Way Galaxy.