Two angles are supplementary if the sum of their measures is equal to 180 degrees. To determine if the given angles \( m\angle A = 37^\circ \) and \( m\angle B = 143^\circ \) are supplementary, we can add the two angle measurements:
\[ m\angle A + m\angle B = 37^\circ + 143^\circ = 180^\circ \]
Since the sum of the angles is exactly 180 degrees, we conclude that the two angles are indeed supplementary.
Reasoning: Supplementary angles are defined as two angles whose measures add up to 180 degrees. In this case, since \( 37 + 143 = 180 \), the two angles meet the definition of supplementary angles.