According to the American colonists, a government is only legitimate if it has consent of the governed. Thus 2nd option is correct.
The term legitimate refers to the conformity with the law. The things or the deeds which are allowed according to the rules and regulations or the laws. For example a legitimate child born to the married couples.
A country can only be legitimate if the people of the specific state are willing to be controlled by a governing body, according to the book American Government: Enduring Principles, Critical Choices.
The American colonists believed that a government could only be considered legitimate if its citizens approved of it. The second choice is the best one.
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