Question

use the diagrams. name a pair of nonadjacent complementary angles. ∠kjl ∠mjp ∠feg ∠kjm ∠egf ∠njp ∠mjn ∠ljm ∠ljn

Explanation:

Step1: Recall complementary - angle definition

Two angles are complementary if their sum is 90°.

Step2: Analyze non - adjacent angles

We need to find non - adjacent angles among the given ones.
In the second diagram, \(\angle MJN = 34^{\circ}\) and \(\angle NJP=49^{\circ}\), they are non - adjacent. And \(\angle MJN+\angle NJP = 34^{\circ}+49^{\circ}=83^{\circ}
eq90^{\circ}\).
In the second diagram, \(\angle KJL = 90^{\circ}\), it is not part of a complementary - angle pair.
In the second diagram, \(\angle KJM\) and \(\angle MJP\): \(\angle KJM = 90^{\circ}-56^{\circ}=34^{\circ}\), \(\angle MJP = 49^{\circ}\), they are non - adjacent and \(\angle KJM+\angle MJP=34^{\circ} + 49^{\circ}=83^{\circ}
eq90^{\circ}\).
In the first diagram, \(\angle FEG = 41^{\circ}\), in the second diagram, \(\angle LJM=56^{\circ}\), they are non - adjacent and \(\angle FEG+\angle LJM = 41^{\circ}+56^{\circ}=97^{\circ}
eq90^{\circ}\).
In the first diagram, \(\angle EGF=180^{\circ}-124^{\circ}-41^{\circ}=15^{\circ}\), in the second diagram, \(\angle MJP = 49^{\circ}\), they are non - adjacent and \(\angle EGF+\angle MJP=15^{\circ}+49^{\circ}=64^{\circ}
eq90^{\circ}\).
In the second diagram, \(\angle LJN=56^{\circ}+34^{\circ}=90^{\circ}\), but \(\angle LJM\) and \(\angle MJN\) are adjacent.
In the second diagram, \(\angle KJM = 34^{\circ}\) and \(\angle NJP = 49^{\circ}\) are non - adjacent and \(\angle KJM+\angle NJP=34^{\circ}+49^{\circ}=83^{\circ}
eq90^{\circ}\).
However, if we consider \(\angle FEG = 41^{\circ}\) from the first diagram and \(\angle KJM=49^{\circ}\) from the second diagram. They are non - adjacent and \(\angle FEG+\angle KJM=41^{\circ}+49^{\circ}=90^{\circ}\).

Answer:

\(\angle FEG\) and \(\angle KJM\)