Final answer:
The newly acquired West was granted popular sovereignty under the Compromise of 1850, allowing residents to decide on the legality of slavery within the territory.
Step-by-step explanation:
The newly acquired West received popular sovereignty as a result of the Compromise of 1850. This compromise was a series of legislative acts intended to ease the tensions between the Northern and Southern states regarding the issue of slavery in new territories won after the Mexican-American War. The fifth and final provision of the Compromise of 1850 allowed the residents of the New Mexico and Utah territories to decide whether to permit slavery, a principle known as popular sovereignty. While the Compromise also included other significant measures, such as admitting California as a free state, adjusting the Texas-New Mexico boundary, abolishing the slave trade in Washington, D.C., and instituting a stricter Fugitive Slave Act, it was this element of popular sovereignty in the new western territories that addressed the student's question directly.