Answer:
The European country that established viceroyalties across Mexico, Central America, and much of South America was Spain.
Explanation:
After the discovery of America in 1492, Spain explored and conquered large tracts of territory in America, from the present southwestern United States, Mexico and the Caribbean, to Central America, most of South America and the northwest coast of North America (now Alaska and British Columbia). All these territories were integrated into the Crown of Castile and, later, into the Spanish Crown.