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.
Answer
Answer:
- ∠GNJ is complementary to ∠JNK.
- ∠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.