Supplementary angles are two angles that add up to 180 degrees. If the measure of angle \( j \) is \( m∠j = 34^\circ \), you can find the measure of angle \( k \) using the equation:
\[ m∠j + m∠k = 180^\circ \]
Substituting the known value:
\[ 34^\circ + m∠k = 180^\circ \]
Now, subtract \( 34^\circ \) from both sides to solve for \( m∠k \):
\[ m∠k = 180^\circ - 34^\circ = 146^\circ \]
Therefore, the measure of angle \( k \) is \( m∠k = 146^\circ \).