What is the measure of the complement of the supplement of a \( 142^{\circ} \) angle? The measure is \( \square^{\circ} \). (Simplify your answer.)

To find the measure of the complement of the supplement of a \( 142^{\circ} \) angle, we first need to determine the supplement of \( 142^{\circ} \). The supplement is calculated as: \[ 180^{\circ} - 142^{\circ} = 38^{\circ} \] Next, we find the complement of \( 38^{\circ} \): \[ 90^{\circ} - 38^{\circ} = 52^{\circ} \] Therefore, the measure of the complement of the supplement of a \( 142^{\circ} \) angle is \( 52^{\circ} \).