When a case is not governed by a statute or other type of law, judges tend to follow the decisions of other judges in similar, prior cases. these similar cases are called

Precedents.

Explanation:

In the legal system, precedents are the decisions of the courts in deciding subsequent cases with similar issues or facts based on the previous court decisions. Common law and equity attaches great importance to the assessment of cases according to consistent rules of theory, so that identical facts produce similar and predictable results. Courts have the power to review and overturn earlier precedents.

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."