Final answer:
The responsibility of Congress in the given options is approving presidential appointments, as the Senate confirms the president's nominees for federal positions.
Step-by-step explanation:
Among the choices given, the responsibility of Congress (legislative branch) is A) Approving presidential appointments. As part of its checks and balances, the U.S. Constitution grants Congress specific powers and responsibilities, including the power to pass legislation and the authority to declare war. Additionally, the Senate, which is part of Congress, has the power to confirm or deny the president's nominees for various federal positions, including federal judges, ambassadors, and the heads of executive departments.