A key Supreme Court ruling that led to the legal end to segregation was.

A: Roe v. Wade.

B: Brown v. Board of Education of Topeka.

C: Plessy v. Ferguson.

D: Miranda v. Arizona.

B: Brown v. Board of Education of Topeka.

The correct answer is B: Brown v. Board of Education of Topeka. To arrive at this answer, one should have a basic understanding of the landmark Supreme Court cases related to segregation in the United States. Here's a breakdown of the steps to reach the correct answer:

1. Start by eliminating the options that are unrelated to segregation cases. Option A, Roe v. Wade, is a significant Supreme Court ruling regarding abortion rights, and is not related to segregation. Option D, Miranda v. Arizona, is a Supreme Court case that established the requirement for police to inform criminal suspects of their rights before questioning them, and is not related to segregation either.

2. Now, you are left with two options: B and C. Plessy v. Ferguson is another important Supreme Court case, but it did not lead to the legal end of segregation. Instead, it established the concept of "separate but equal" in 1896, which allowed for racial segregation as long as separate facilities were provided. Therefore, you can eliminate option C.

3. By the process of elimination, the only remaining option is B: Brown v. Board of Education of Topeka. This landmark case, decided in 1954, declared racial segregation in public schools as unconstitutional. It overturned the previous doctrine of "separate but equal" established by Plessy v. Ferguson and laid the foundation for desegregation efforts in the United States.

Hence, the key Supreme Court ruling that led to the legal end of segregation was Brown v. Board of Education of Topeka.

The key Supreme Court ruling that led to the legal end to segregation was B: Brown v. Board of Education of Topeka.