One reason for the united states’ interest in the open door policy for china was that it had just taken possession of which region, after the spanish-american war?

 The Philippines

Further detail:  The United States had taken possession of the Philippines, as well as Guam and Puerto Rico, in 1898, after winning the Spanish-American War.   So US interest in Asia was heightened.  At the same time, other nations had begun competing for "spheres of influence" in trade access with China.

The Open Door policy was issued by the United States in 1899-1900 as a series of dispatches from the US Secretary of State to other nations that had trading interests in China --  Great Britain, Germany, France, Italy, Japan, and Russia.  The policy reasserted earlier agreements that all countries should have equal access to ports in China, without undue preference to "spheres of influence" for one nation or another.  The United States was seeking to maintain an equal footing with other nations in the access to trade in China.

lying without the limits of the several states; and may permit them, at such times, and in such manner as it

true

explanation: