Question

Find the supplement of an angle with the given measures.

Answer 1

The supplement of an angle will be its difference from 180° (or -180°). Hence your supplements are
.. -37° ⇒ -143° or 217°
.. -9° ⇒ -171° or 189°
.. -84° ⇒ -96° or 264°

Since you allow angles to be negative, I'd probably choose the negative value as the supplement.

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If you're going to define angles in such a way as to allow their measures to be negative, then you need to make a corresponding definition of complement and supplement. One definition I've seen of "supplement" is that it meets the requirements that
.. sin(θ) = sin(supplement(θ))
.. cos(θ) = -cos(supplement(θ))

The above angles (either positive or negative) will meet these requirements.