Final answer:
The Indian Reorganization Act (IRA) replaced the Dawes Act of 1887 and returned lands to the control of tribes, supporting the preservation of Indian cultures.
Step-by-step explanation:
The measure that replaced the Dawes Act of 1887 and returned lands to the control of tribes and supported preservation of Indian cultures was the Indian Reorganization Act (IRA).
The IRA, also known as the Wheeler-Howard Act, was passed in 1934 and aimed to reverse the assimilation policies of the Dawes Act. It restored tribal ownership of land and provided funds to help tribes purchase some of the lands they had lost in the past. The IRA also promoted self-government and the preservation of Native American cultures.
Overall, the Indian Reorganization Act was a significant shift in policy that recognized the importance of tribal sovereignty and cultural preservation.