What was the name of the law in which the government gave a 160 acre farm to anyone willing to work on and improve that land

The Homestead Act is the answer you're looking for

Homestead Act was the name of the law in which the government gave a 160 acre farm to anyone willing to work on and improve the land. The correct option among all the options given in the question is option "D". According to the Homestead Act, the land was given almost free of cost and the only thing the person had to do was develop the land for farming and build a house.
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