Question

→←
jl and →←
mo are parallel lines.
which angles are adjacent angles?
∠mnk and ∠jki
∠mnk and ∠lki
∠mnk and ∠onp
∠mnk and ∠onk

Explanation:

To determine adjacent angles, we use the definition: adjacent angles are two angles that share a common side and a common vertex, and do not overlap.

Step 1: Analyze each option

• For $\angle MNK$ and $\angle JKI$: These angles do not share a common side or vertex. $\angle MNK$ has vertex $N$, $\angle JKI$ has vertex $K$. So they are not adjacent.
• For $\angle MNK$ and $\angle LKI$: $\angle MNK$ has vertex $N$, $\angle LKI$ has vertex $K$. No common side or vertex. Not adjacent.
• For $\angle MNK$ and $\angle ONP$: These are vertical angles (opposite angles formed by intersecting lines), not adjacent.
• For $\angle MNK$ and $\angle ONK$: They share the common side $NK$ and the common vertex $N$. Also, they do not overlap. So they meet the criteria for adjacent angles.

Answer:

$\angle MNK$ and $\angle ONK$