Final answer:
James K. Polk was the President of the United States when Texas was annexed in 1845, transforming from the Lone Star Republic to a U.S. state.
Step-by-step explanation:
When Texas became annexed by the United States, James K. Polk was serving as President. Texas was an independent nation known as the Lone Star Republic from 1836 to 1846 after electing Sam Houston as its first president. Amid varying attitudes towards annexation due to political tensions with Mexico and the issue of slavery, Texas ultimately joined the Union, with the U.S. formally recognizing the annexation during Polk's presidency. The annexation of Texas and its boundary dispute with Mexico would later be a significant factor leading to the Mexican-American War.