Which compromise involved New Mexico and Utah using popular sovereignty to determine their status on slavery?

The Compromise of 1850 is the correct answer because it specifically addressed the status of slavery in the territories acquired from Mexico, which included New Mexico and Utah. The Compromise introduced the concept of popular sovereignty, allowing the residents of these territories to vote on whether to permit slavery within their borders. This was part of a broader compromise to alleviate tensions between free and slave states following the Mexican-American War.

The significance of popular sovereignty is that it shifted the decision-making power regarding slavery from Congress to the territorial residents themselves, a practical solution aimed at pacifying both pro-slavery and anti-slavery factions. The Compromise of 1850 also included other key measures, such as the admission of California as a free state and the enactment of a stricter fugitive slave law, further illustrating the complex negotiations necessary to maintain the balance between slave and free states during this period of American history.

In contrast, other choices such as the Missouri Compromise, the Compromise of 1820, and the Kansas-Nebraska Act pertain to different states or concepts of slavery that do not directly apply to the territories of New Mexico and Utah under the framework employed in the Compromise of 1850.