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After the Senate rejected the Texas annexation treaty, proponents of annexation decided to gain Texas by a joint resolution of Congress, which required only a majority vote in each house. Passed by the House (120–98) and Senate (27–25) in 1845, the resolution was later challenged but upheld by the Supreme Court.
Congress doth consent that the territory properly included within and rightfully belonging to the Republic of Texas may be erected into a new State, to be called the State of Texas
Records of the U.S. Senate, National Archives and Records Administration