line jm intersects line gk at point n. which statements are true about the figure? select two options. ∠gnj…

line jm intersects line gk at point n. which statements are true about the figure? select two options. ∠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.

line jm intersects line gk at point n. which statements are true about the figure? select two options. ∠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

Answer:

  1. ∠GNJ is complementary to ∠JNK.
  2. ∠MNL is complementary to ∠KNL.

Explanation:

Step1: Recall angle - relationship definitions

Complementary angles add up to 90°, supplementary angles add up to 180°.

Step2: Analyze ∠GNJ and ∠JNK

Since line JM and line GK intersect at N and ∠GNM = 90° (right - angle), ∠GNJ+∠JNK = 90°, so they are complementary.

Step3: Analyze ∠MNL and ∠KNL

∠MNK = 90° (right - angle), so ∠MNL+∠KNL = 90°, they are complementary.

Step4: Analyze ∠MNG and ∠GNJ

∠MNG+∠GNJ = 180°, they are supplementary, not complementary.

Step5: Analyze ∠KNJ and ∠MNL

There is no relationship such that ∠KNJ+∠MNL = 180°.

Step6: Analyze ∠GNM and ∠JNK

∠GNM = 90° and ∠JNK is not 90°, so they are not supplementary.