Which compromises allowed California to enter the union as a free state while the southwestern territories could decide the slavery issue on their own?

The Compromise of 1850 facilitated California's admission as a free state while allowing the newly acquired southwestern territories—New Mexico and Utah—to decide the slavery issue through popular sovereignty. This compromise aimed to balance the interests of free and slave states, easing tensions between the North and South. Additionally, it included provisions such as the Fugitive Slave Act, which strengthened the enforcement of returning escaped slaves, appeasing Southern states. Overall, these compromises were pivotal in temporarily alleviating sectional conflict.