The u. s. supreme court consists of the chief justice and how many associate judges?

Eight Associate Justices join the Chief Justice on the Supreme Court. 

The number of Supreme Court Justices is not set by the US Constitution.  Article III, Section 1 simply states:  "The judicial Power of the United States, shall be vested in one supreme Court, and in such inferior Courts as the Congress may from time to time ordain and establish."  Congress establishes the number of Justices on the Supreme Court.  The current number of nine total Justices was set by the Judiciary Act of 1869.  Prior to that, there were at times as few as six Supreme Court Justices.

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