Final answer:
The two modern day countries that were part of the British Empire in Africa are Egypt and Sudan (option b).
Step-by-step explanation:
The two modern day countries that used to be part of the United Kingdom (British Empire) in Africa are Egypt and Sudan. This corresponds to option b of the question presented. In the historical context, after the fall of the Ottoman Empire, Britain gained control over Egypt and parts of Sudan, both prized for their rich natural resources which included gold, ebony and ivory. The influence of the British and other European powers in Africa was broadly established following agreements such as the 1884 Berlin Conference that divided African territories among European colonizers. Many of these arbitrarily drawn boundaries have persisted into the present-day borders of African nations.