Final answer:
The Republic of Texas agreed to become part of the United States after winning independence to gain protection, economic benefits, and to be part of a larger American destiny.
Step-by-step explanation:
The Republic of Texas agreed to become part of the United States after winning independence for several reasons. One of the main reasons was the desire for protection against potential Mexican retaliation. Texas feared that remaining an independent nation would make them vulnerable to invasion from Mexico. By joining the United States, Texas could rely on the military and political support of a larger and more powerful nation. Another reason was the economic benefits of becoming part of the United States. Texas had a vast amount of land, and by joining the United States, they could attract more American settlers for economic development. Additionally, the prospect of joining an expanding nation appealed to many Texans who saw themselves as part of a larger American destiny.