President johnson challenged the tenure of office act by

Attempting to fire the Secretary of War, Edwin Stanton.

Explanation:

As Johnson and Stanton collided about some south states that were still using black people as slaves, Johnson tried to remove him as secretary, ignoring both the congress and a law that was passed to prevent Stanton to being fired. He impeached the president but, when Johnson was jugded acquitted of any wrongdoing, Stanton voluntarily resigned.  

He was attempting to challenge the constitutionality of the law created by Congress to limit Executive Branch power

Explanation:

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answer; utilitarian;