Final answer:
The problem of both Great Britain and the United States claiming Oregon was resolved through negotiations and diplomacy, with the boundary line along the 49th parallel being accepted.
Step-by-step explanation:
The problem of both Great Britain and the United States claiming Oregon was resolved through negotiations and diplomacy.
Initially, both countries based their claims on prior discovery, exploration, and treaty rights. The two countries reached an agreement in 1818 for a ten-year joint occupation of Oregon, which was renewed in 1827.
In the 1840s, the United States saw a significant increase in American settlers migrating to Oregon. This strengthened the U.S. claim to the region. Eventually, President Polk negotiated with Great Britain and accepted the boundary line along the 49th parallel, dividing Oregon between the two countries.