The United States involved itself in Vietnam in the 1960s because:

A. The American people demanded the government support Vietnam

B. American Businesses in Vietnam were threatened by the communist

C. It feared that if Vietnam became communist then surrounding countries would quickly follow it feared that is Vietnam became communist then surrounding countries would quickly follow.

D. Japan was threatened militarily by the possibility of a communist government in Vietnam.

To determine the reason why the United States involved itself in Vietnam in the 1960s, we can analyze each answer option and see which one aligns with historical facts:

A. The American people demanded the government support Vietnam: This option suggests that the American public's demand was the driving force behind the U.S. involvement. However, it is important to note that while there were anti-communist sentiments among some American citizens, the majority did not push for direct U.S. involvement in Vietnam. Therefore, this option is not the primary reason for U.S. involvement.

B. American Businesses in Vietnam were threatened by the communist: While the protection of American businesses can be a factor in global politics and foreign interventions, it was not a primary reason for the U.S. involvement in Vietnam. Therefore, this option is not the primary reason either.

C. It feared that if Vietnam became communist, then surrounding countries would quickly follow: This option relates to the Domino Theory, which was a prominent rationale for U.S. involvement in Vietnam. The Domino Theory argued that if one country in Southeast Asia fell to communism (like Vietnam), neighboring countries would also fall like dominos. This fear of the spread of communism was a significant reason why the United States intervened in Vietnam. Therefore, this option is the primary reason for U.S. involvement.

D. Japan was threatened militarily by the possibility of a communist government in Vietnam: While Japan had significant economic interests in Southeast Asia, including Vietnam, the direct military threat Japan faced from a communist government in Vietnam was not the primary reason for U.S. involvement. Therefore, this option is not the primary reason either.

In conclusion, the correct answer is option C. The United States involved itself in Vietnam in the 1960s because it feared the spread of communism to surrounding countries if Vietnam became communist, based on the Domino Theory.