Question

use the diagrams. name a pair of adjacent supplementary angles.

Explanation:

Adjacent supplementary angles share a common side and their sum is 180 degrees. In the diagram, we look for such pairs. Angle $\angle EGF$ and $\angle FGH$ share side $\overrightarrow{GF}$ and $\angle EGF+\angle FGH = 41^{\circ}+124^{\circ}=165^{\circ}
eq180^{\circ}$. In the second - diagram, $\angle LJM$ and $\angle MJN$ share side $\overrightarrow{JM}$, and $\angle LJM = 56^{\circ}$, $\angle MJN=34^{\circ}$, $\angle LJM+\angle MJN = 90^{\circ}
eq180^{\circ}$. However, $\angle KJL$ and $\angle LJM$ share side $\overrightarrow{JL}$, and since $\angle KJL = 90^{\circ}$ and $\angle LJM = 90^{\circ}$, $\angle KJL+\angle LJM=180^{\circ}$.

Answer:

$\angle KJL$ and $\angle LJM$