What treaty was signed by the United Kingdom and President James Polk?
Oregon Bill of 1848:  It was enacted by the 30th United States Congress, and signed by President James K. Polk. Oregon Treaty: The Oregon Treaty is a treaty between the United Kingdom and the United States that was signed on June 15, 1846, in Washington, D.C. Signed under the presidency of James K. Polk, the treaty brought an end to the Oregon boundary dispute by settling competing American and British claims to the Oregon Country; the area had been jointly occupied by both Britain and the U.S. since the Treaty of 1818.
Oregon Treaty