Answer:
The core idea that both Franklin Roosevelt’s New Deal and policies from the Progressive Era shared was:
option D: the government has a responsibility to protect the well-being of its citizens
Explanation:
New Deal was President Roosevelt's promise to the people of America that he would being the country out if the Great Depression. His New deal was about relief and reform during the crashing time.
The Progressive Era worked on bringing more transparent and stronger government which would have policies like civil service reform and food safety laws and so on. It also protected rights of women and U.S. workers.
Thus, the core idea for both policies was to protect the well being of its citizens.