Answer:
The outgoing Tyler administration secured the annexation of Texas in the winter of 1844-1845 by a joint resolution of Congress. This resolution, which was passed by both the House of Representatives and the Senate, authorized the annexation of Texas and made it a part of the United States. The annexation was controversial at the time, as it raised questions about the expansion of slavery and the balance of power between free and slave states in the Union. However, it was ultimately approved and Texas became the 28th state of the United States on December 29, 1845. Option B, joint resolution of Congress, is the correct answer.