Question

Line JM intersects line GK at point N Which statements are true about the figure? Check all that apply.

Answer 1

B. and E.

Hope this Helps!

Answer 2

we know that

Complementary angles are two angles whose sum is equal to $90$°, while supplementary angles are two angles whose sum is equal to $180$°.

So

Statements

case 1) GNJ is complementary to JNK

Is False

Angle GNJ is $90$ degrees and angle JNK is $90$ degrees. The sum of the angles GNJ and JNK is $180$ degrees. Therefore, GNJ is not complemetary to JNK.

$angle\ GNJ+angle\ JNK=180\ degrees$

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 $90$ degrees. Therefore, MNL is complementary to GNJ.

$angle\ MNL+angle\ KNL=90\ degrees$

MNL is complementary to KNL

case 3) MNG is complementary to GNJ

Is False

Angle MNG is $90$ degrees and angle GNJ is $90$ degrees. The sum of the angles MNG and GNJ is $180$ degrees. Therefore, MNG is not complemetary to GNJ.

$angle\ MNG+angle\ GNJ=180\ degrees$

MNG is supplementary to GNJ, not complementary

case 4) KNJ is supplementary to MNL

Is False

Angle KNJ is $90$ degrees and angle MNL is less than $90$ degrees. The sum of the angles KNJ and MNL is less than $180$ degrees. Therefore, KNJ is not supplementary to MNL

$angle\ KNJ+angle\ MNL < 180\ degrees$

case 5) GNM is supplementary to JNK

Is True

Angle GNM is $90$ degrees and angle JNK is $90$ degrees. The sum of the angles GNM and JNK is $180$ degrees. Therefore, GNM is supplementary to JNK.

$angle\ GNM+angle\ JNK = 180\ degrees$

GNM is supplementary to JNK

therefore

the answer is

MNL is complementary to KNL

GNM is supplementary to JNK