Final answer:
King Charles I (Charles V of the Holy Roman Empire) controlled the Spanish empire, which included Spain, Portugal (after his wife's death), and their colonies in the Americas. Spain and Portugal were the first to colonize the Americas, legitimized by the Treaty of Tordesillas. By the seventeenth century, Spain had the largest empire in the Americas. The option (a) is correct.
Step-by-step explanation:
When King Charles I inherited the Spanish throne, the Spanish empire included Spain and its colonies in the Americas. It was King Charles V, also known as Charles I of Spain, who became ruler of both the Spanish and Portuguese empires due to inheritance and marriage, thereby controlling vast territories which included Spain (and subsequently Portugal upon the death of his wife Isabella), their European possessions like the "Spanish Netherlands", and their expansive colonies in the Americas which were established following the initial colonization and conquests of Indigenous empires such as the Aztecs, Inca, and Maya.
Spain and Portugal were the first countries to establish colonies in the Americas, and their imperial domains were legitimized by the Treaty of Tordesillas, which the Pope sanctioned, dividing the New World between them. Other European nations like England and the Netherlands did not recognize this treaty and later established their colonies in the Americas and other parts of the world. The Spanish empire was the largest among the European powers in the early seventeenth century. Therefore, option (a) is correct.