Final answer:
The two territorial provisions in the Compromise of 1850 that settled California's petition for admission as a free state were the establishment of popular sovereignty in the territories and the division of the Mexican Cession into the territories of New Mexico and Utah.
Step-by-step explanation:
The two territorial provisions in the Compromise of 1850 that settled California's petition for admission as a free state were:
- The establishment of popular sovereignty in the territories: This meant that the people in the territories of New Mexico and Utah would decide for themselves whether to allow slavery or not. It followed the democratic principle of majority rule.
- The division of the Mexican Cession into the territories of New Mexico and Utah: This division organized and defined the boundaries of the new territories created from the Mexican Cession.