How did sam houston persuade the united states to annex texas?
a. by claiming that texas would rejoin mexico to settle its debts
b. by threatening to ask france for if the united states refused
c. by threatening to ask britain for if the united states refused
d. by starting a border dispute with mexico to gain new territory

Correct

C.by threatening to ask Britain for help if the United States refused.

Texas had been a part of Mexico since Mexico won its independence from Spain in 1821. But there was plenty of tension between the Mexican government and the territory of Texas. Texas declared its independence from Mexico in 1836, and under the leadership of Sam Houston, defeated the Mexican army at the Battle of San Jacinto in April of that year. However, the Mexican government continued to refuse official recognition of Texas' independence.

When the Republic of Texas was established in 1836, the citizens of the newly independent country voted for Sam Houston as their president ... but also voted their endorsement of Texas becoming part of the United States.  There was plenty of delay before that happened, however, because there was question and controversy over whether or not Texas would enter the Union as a slave state. 

In the process of those long negotiations, the government of Texas had also looked to Great Britain for possible support in its ongoing tensions with Mexico. In 1843, Sam Houston's administration in Texas was considering making a deal with the Mexican government that would allow Texas to govern itself but with some connection to Mexico. They would have asked Great Britain to act as mediator in negotiating with Mexico.

Ultimately, however, the United States Congress did finally vote for acceptance of Texas as a state in 1844. In 1845, Texas entered the US as the 28th state ... and permitted as a slave state.

with my knoladg i would say it was c