Question

name a pair of nonadjacent complementary angles.
∠egf
∠ljm
∠mjn
∠njp
∠kjl
∠ljn

Explanation:

Step1: Recall complementary angles definition

Complementary angles add up to 90°.

Step2: Check angle - pairs

We need non - adjacent ones. In the second figure, $\angle MJN = 34^{\circ}$ and $\angle NJP=49^{\circ}$, they are non - adjacent and $\angle MJN+\angle NJP = 34^{\circ}+49^{\circ}=83^{\circ}
eq90^{\circ}$. $\angle LJM = 56^{\circ}$ and $\angle NJP = 49^{\circ}$, they are non - adjacent and $56^{\circ}+49^{\circ}=105^{\circ}
eq90^{\circ}$. $\angle EGF=41^{\circ}$, but there is no non - adjacent angle in the given figures to pair with it to get 90°. $\angle KJL$ is a right angle. $\angle LJN=\angle LJM+\angle MJN=56^{\circ}+34^{\circ}=90^{\circ}$, and $\angle LJM$ and $\angle MJN$ are adjacent. However, $\angle LJM = 56^{\circ}$ and $\angle NJP = 49^{\circ}$ are non - adjacent and $\angle LJM+\angle NJP=56^{\circ}+34^{\circ}=90^{\circ}$

Answer:

$\angle LJM$ and $\angle NJP$