To determine if the two angle measurements \( m\angle A = 37^\circ \) and \( m\angle B = 143^\circ \) can be supplementary, we need to check if their sum is equal to \( 180^\circ \).
Calculating the sum: \[ m\angle A + m\angle B = 37^\circ + 143^\circ = 180^\circ \]
Since \( 37^\circ + 143^\circ = 180^\circ \), the angles do indeed add up to \( 180^\circ \).
Therefore, the correct answer is:
C. Yes, they are a supplementary pair.