Final answer:
The Treaty of Augsburg is the 1555 agreement declaring that its ruler would decide the religion of each German state.
Step-by-step explanation:
The 1555 agreement declaring that its ruler would decide the religion of each German state is called the Treaty of Augsburg. This treaty was reached at the Diet of Augsburg in 1555, during the time of the Protestant Reformation. It granted rulers in the Holy Roman Empire the right to choose between Lutheranism or Catholicism as the official religion in their respective states.