Question

ir and ln are parallel lines.
which angles are vertical angles?
∠lmj and ∠nmj ∠nmj and ∠nmo
∠lmo and ∠nmj ∠lmj and ∠kjh

Explanation:

Step1: Recall vertical angles definition

Vertical angles are opposite angles formed by two intersecting lines, and they are equal in measure.

Step2: Analyze each option

• Option 1: $\angle LMJ$ and $\angle NMJ$: These two angles share a common side $MJ$ and their non - common sides are in a straight line (since $LN$ is a straight line), so they are supplementary (form a linear pair), not vertical angles.
• Option 2: $\angle NMJ$ and $\angle NMO$: These two angles share a common side $NM$ and their non - common sides are in a straight line (since $HO$ is a straight line), so they are supplementary (form a linear pair), not vertical angles.
• Option 3: $\angle LMO$ and $\angle NMJ$: When lines $HO$ and $LN$ intersect at $M$, $\angle LMO$ and $\angle NMJ$ are opposite angles formed by the intersection of the two lines. So they are vertical angles.
• Option 4: $\angle LMJ$ and $\angle KJH$: $\angle LMJ$ is at point $M$ and $\angle KJH$ is at point $J$, and they are not formed by the same pair of intersecting lines, so they are not vertical angles.

Answer:

$\angle LMO$ and $\angle NMJ$