For an angle to be supplementary to another angle, they must be equal to 180. Angles 6, 10, 13, and 9 are all supplementary to angle 16. This is because angle 16 is supplementary to angle 9 by the Same Side Interior Angles Theorem, which makes it supplementary to angle 10 by the Alternate Exterior Angles Theorem, which is also congruent to angle 13 by the Vertical Angles Theorem, which is also supplementary to angle 6 by the Alternate Exterior Angles Theorem.
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