∠KLN and ∠MLN for adjacent angles with vertex L and common arm LN.
How to determine adjacent angles.
Adjacent angles are two angles that share a common arm (side) and a common vertex, yet do not overlap. In other words, they are side by side and do not share any interior points.
From the given options
∠KLN and ∠MLN have common arm LN and share the same vertex at L, so they are adjacent angles.
∠KLN and ∠HIL have different vertices at L and I respectively. so, they are not adjacent.
∠KLN and ∠HIG have different vertices at L and I. They are not adjacent angles.
∠KLN and ∠MLI have same vertex at L but different arms. ∠KLN has arm LN and ∠MLI has arm LI. so, they are not adjacent angles rather they are vertical angles.
Therefore, ∠KLN and ∠MLN for adjacent angles with vertex L and common arm LN.