What do you mean by check and balance?

Checks and balances is a principle of government under which separate branches are empowered to prevent actions by other branches and are induced to share power. Checks and Balances are meant to keep power distributed rather than having one area of government holding too much power.

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d. i assume the underlined word is "role." reformat if it isn't.

explanation:

role is closest to part because when replacing words, "playing a vital decision," "playing a vital activity," and "playing a vital dollar" don't make logical sense. the only meaningful choice is "playing a vital part."

this fits one of merriam-webster's definitions of role: "a function or part performed especially in a particular operation or process."