Final answer:
Texas joined the U.S. after the 1844 presidential election indicated public support for annexation, leading to its eventual annexation in 1845 and the subsequent Mexican-American War due to border disputes.
Step-by-step explanation:
Texas became part of the U.S. after a series of events. Initially, after Texas declared its independence from Mexico in 1836, the region operated as the Lone Star Republic. Although the U.S. recognized Texas as an independent nation, the fear of annexing Texas causing political tensions with Mexico was present. Nonetheless, many Texans and expansionists in the slaveholding South aimed for annexation to the United States as they saw it as a way to expand westward and support their interests in slavery.
The U.S. was initially reluctant to annex Texas due to the potential for conflict with Mexico and the issue of slavery. The concern included inciting a war with Mexico and the impact of admitting a new slave state on the balance between free and slave states in Congress. However, in the 1844 presidential election, public support for annexation was indicated, and soon after President James K. Polk's administration took over, Texas was annexed in 1845. This led to the Mexican-American War, due to disagreements over the boundary between Texas and Mexico, with the U.S. claiming the Rio Grande and Mexico the Nueces River.
In summary, the reason Texas was annexed to the U.S. aligns most closely with option C from the question: After the 1844 presidential election showed public support for annexation. This was followed by Congress passing a resolution to annex Texas during the days after the election and before Polk's inauguration.