Final answer:
Britain recognized Rhodesia's independence in 1980 after an agreement was reached for majority rule, ending a civil war and beginning Zimbabwe's independence under Prime Minister Robert Mugabe.
Step-by-step explanation:
Britain did not allow for the white Rhodesian government to become independent until there had been an agreement to transition to majority rule, incorporating the black African population in the government. This came after a prolonged struggle, which included a unilateral declaration of independence in 1965 by the white-dominated Rhodesian government led by Ian Smith. However, due to lack of international recognition and imposed sanctions by the United Nations, this was not acknowledged by Britain. Following a civil war and lengthy negotiations, Britain recognized the independence of Zimbabwe in 1980, after an agreement was reached that included black African leaders, leading to Robert Mugabe becoming the prime minister.