Final answer:
Portugal is the country that has the Madeira Archipelago southeast of it, off the coast of Northwest Africa.
Step-by-step explanation:
The country that has the Madeira Archipelago southeast of it off the coast of Northwest Africa is Portugal. The Madeira Islands, along with the Azores and the Cape Verde Islands, were significant in the expansion of the Portuguese maritime empire. Portuguese mariners, guided by Prince Henry commonly known as "the Navigator", utilized these islands as a strategic base for further explorations and to establish trading routes. As a result, Portugal was able to extend its reach down the western coast of Africa, around to India, and across the Atlantic to Brazil.