Question

ik and ln are parallel lines. which angles are supplementary angles? ∠lmj and ∠lmo ∠lmj and ∠ijh ∠lmj and ∠nmo ∠lmj and ∠kjm

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\).

Step2: Analyze \(\angle LMJ\) and \(\angle KJM\)

Since \(\overleftrightarrow{KN}\) and \(\overleftrightarrow{IK}\) are parallel lines and \(OH\) is a transversal. \(\angle LMJ\) and \(\angle KJM\) form a linear - pair. A linear - pair of angles is supplementary. That is \(\angle LMJ+\angle KJM = 180^{\circ}\) (because they are adjacent angles and their non - common sides form a straight line).

Step3: Analyze other options

• For \(\angle LMJ\) and \(\angle LMO\): There is no such relationship (like linear - pair or other angle - sum relationships based on parallel lines and transversals) that would make their sum \(180^{\circ}\).
• For \(\angle LMJ\) and \(\angle IJH\): \(\angle IJH\) and \(\angle KJM\) are vertical angles (\(\angle IJH=\angle KJM\)), but \(\angle LMJ+\angle IJH

eq180^{\circ}\) (since \(\angle LMJ+\angle KJM = 180^{\circ}\) and \(\angle IJH=\angle KJM\) would be wrong in terms of the sum if we consider them directly without the linear - pair concept).

• For \(\angle LMJ\) and \(\angle NMO\): There is no property (such as linear - pair, or angle - sum properties from parallel lines) that gives \(\angle LMJ+\angle NMO = 180^{\circ}\).

Answer:

\(\angle LMJ\) and \(\angle KJM\)