How did Texas separate from Mexico?

The Republic of Texas was annexed by the United States on December 29, 1845. After a protracted dispute between the U.S. and Mexico over the annexation, the Mexican–American War began in 1846. Mexico officially recognized Texas as part of the U.S. in the 1848 Treaty of Guadalupe Hidalgo, ceding also most of what are now the southwestern United States including California, Utah, and Nevada along with parts of Wyoming, Arizona, Colorado and New Mexico in exchange for payment for damages done during the conflict and assumption of American claims against Mexican citizens