we know that
Complementary angles are two angles whose sum is equal to [tex] 90 [/tex]°, while supplementary angles are two angles whose sum is equal to [tex] 180 [/tex]°.
So
Statements
case 1) GNJ is complementary to JNK
Is False
Angle GNJ is [tex] 90 [/tex] degrees and angle JNK is [tex] 90 [/tex] degrees. The sum of the angles GNJ and JNK is [tex] 180 [/tex] degrees. Therefore, GNJ is not complemetary to JNK.
[tex] angle\ GNJ+angle\ JNK=180\ degrees [/tex]
GNJ is supplementary to JNK, not complementary
case 2) MNL is complementary to KNL
Is True
The sum of angles MNL and KNL is MNK which is [tex] 90 [/tex] degrees. Therefore, MNL is complementary to GNJ.
[tex] angle\ MNL+angle\ KNL=90\ degrees [/tex]
MNL is complementary to KNL
case 3) MNG is complementary to GNJ
Is False
Angle MNG is [tex] 90 [/tex] degrees and angle GNJ is [tex] 90 [/tex] degrees. The sum of the angles MNG and GNJ is [tex] 180 [/tex] degrees. Therefore, MNG is not complemetary to GNJ.
[tex] angle\ MNG+angle\ GNJ=180\ degrees [/tex]
MNG is supplementary to GNJ, not complementary
case 4) KNJ is supplementary to MNL
Is False
Angle KNJ is [tex] 90 [/tex] degrees and angle MNL is less than [tex] 90 [/tex] degrees. The sum of the angles KNJ and MNL is less than [tex] 180 [/tex] degrees. Therefore, KNJ is not supplementary to MNL
[tex] angle\ KNJ+angle\ MNL < 180\ degrees [/tex]
case 5) GNM is supplementary to JNK
Is True
Angle GNM is [tex] 90 [/tex] degrees and angle JNK is [tex] 90 [/tex] degrees. The sum of the angles GNM and JNK is [tex] 180 [/tex] degrees. Therefore, GNM is supplementary to JNK.
[tex] angle\ GNM+angle\ JNK = 180\ degrees [/tex]
GNM is supplementary to JNK
therefore
the answer is
MNL is complementary to KNL
GNM is supplementary to JNK
