Final answer:
The Supreme Court established the authority to determine the constitutionality of congressional acts by its ruling in Marbury v. Madison. Chief Justice John Marshall, in his opinion, declared that the part of the Judiciary Act of 1789 granting the Court the power to issue writs of mandamus was unconstitutional, establishing the principle of judicial review.
Step-by-step explanation:
The Supreme Court established the authority to determine the constitutionality of congressional acts by its ruling in Marbury v. Madison. This landmark case, decided in 1803, involved an appointed justice named William Marbury who sought a legal remedy after not receiving his commission. Chief Justice John Marshall, in his opinion, declared that the part of the Judiciary Act of 1789 granting the Court the power to issue writs of mandamus was unconstitutional, establishing the principle of judicial review.