Final answer:
The United States acquired California, Arizona, New Mexico, Nevada, Colorado, Utah, and part of Wyoming after defeating Mexico.
Step-by-step explanation:
The United States acquired several territories after defeating Mexico in the Mexican-American War. The Treaty of Guadalupe Hidalgo, signed in 1848, resulted in Mexico ceding all of their territory north of the Rio Grande River to the United States. This included the areas that now make up the states of California, Arizona, New Mexico, Nevada, Colorado, Utah, and part of Wyoming. The U.S. also negotiated the Gadsden Purchase in 1854, acquiring the Mesilla Valley in present-day Arizona.