Question

which angles are alternate exterior angles?
∠nmj and ∠kjh
∠ijh and ∠ijm
∠lmo and ∠kjh
∠lmj and ∠nmj

Explanation:

Step1: Recall Alternate Exterior Angles Definition

Alternate exterior angles are formed when a transversal crosses two parallel lines (or lines cut by a transversal). They lie outside the two lines and on opposite sides of the transversal.

Step2: Analyze Each Option

• Option 1: $\angle NMJ$ and $\angle KJH$ - Check their positions. $\angle NMJ$ is inside the lines, not exterior. Eliminate.
• Option 2: $\angle IJH$ and $\angle IJM$ - These are adjacent angles, not alternate exterior. Eliminate.
• Option 3: $\angle LMO$ and $\angle KJH$ - $\angle LMO$ is outside the two lines (formed by transversal $HO$ and lines $LK$ and $IJ$), $\angle KJH$ is also outside, on opposite sides of transversal $HO$. This fits alternate exterior angles.
• Option 4: $\angle LMJ$ and $\angle NMJ$ - These are adjacent angles on a straight line, not alternate exterior. Eliminate.

Answer:

$\angle LMO$ and $\angle KJH$ (the option with $\angle LMO$ and $\angle KJH$)