Question

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

GNJ is complementary to JNK.
MNL is complementary to KNL.
MNG is complementary to GNJ.
KNJ is supplementary to MNL.
GNM is supplementary to JNK

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