Final answer:
In the case of students challenging their school's rule on wearing armbands in protest, the Supreme Court set a precedent supporting the students' First Amendment rights in Tinker v. Des Moines.
Step-by-step explanation:
In the case where students challenged their school's rule on wearing armbands in protest, the precedent set by the Supreme Court supporting the students' First Amendment rights was Tinker v. Des Moines. In this case, the Supreme Court held that the students' wearing of armbands as a form of protest was protected speech under the First Amendment. The Court ruled that students do not lose their First Amendment rights when they enter the school property, unless their speech substantially disrupts the operation of the school.