The roosevelt corollary was an extension of which of the following policies?

It was an extension of the Monroe Doctrine.

Explanation:

The Roosevelt Corollary was set forth by President Theodore Roosevelt in 1904 (in his State of the Union Address that year).  It was a tweaking of the Monroe Doctrine.  The Monroe Doctrine expressed US opposition to European interference in the Americas.  Roosevelt's corollary to that doctrine was that the United States would intervene in conflicts between European countries and Latin American countries, rather than having the Europeans press their claims directly.

The issue that started this concern was a financial crisis in the Dominican Republic, whose government had stopped payments on millions of dollars in debt to various nations.  There was concern that European powers would seek to come to the Western Hemisphere to collect debts and then maybe also set themselves up as occupying powers in countries in the region.  It allowed the US to maintain the primary position of power in the Western Hemisphere.