For Question 1, the correct response is:
The United States annexed Texas.
The annexation of Texas by the United States in 1845 was a significant catalyst for the Mexican-American War, as Mexico still considered Texas a part of its territory.
For Question 2, the correct response is:
It gave the United States territory known as the Mexican Cession.
The Mexican-American War resulted in the signing of the Treaty of Guadalupe Hidalgo, which ceded a vast amount of territory to the United States, including present-day California, Arizona, New Mexico, Nevada, Utah, and parts of Colorado and Wyoming, collectively known as the Mexican Cession.