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.

Question

24-08-2017
Mathematics

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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.

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nobillionaireNobley nobillionaireNobley · Answer 1 · 2017-08-31T16:36:56+02:00

Two angles are said to be complementary when their sum is 90 degrees and are said to be supplementary when their sum is 180 degree.

From the figure, line JM intersects line GK at 90 degrees, hence

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.

The sum of angles MNL and KNL is MNK which is 90 degrees. Therefore, MNL is complementary to GNJ.

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 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 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.

Therefore, the true statements are:
MNL is complementary to GNJ.
and
GNM is supplementary to JNK.