Question

name the marked angle in 2 different ways.

Explanation:

Step1: Identify the vertex and rays

The marked angle has vertex \( L \), and the two rays forming it are \( LM \) and \( LN \) (or \( LM \) and \( LK \)? Wait, looking at the diagram, the marked angle is at \( L \), between \( LM \) and \( LN \)? Wait, no, the points are \( K \), \( N \), \( M \), \( L \). So the marked angle is at \( L \), with sides \( LM \) and \( LN \)? Wait, no, the angle is between \( LM \) and \( LL \)? No, the angle is at \( L \), with one side from \( L \) to \( M \) and the other from \( L \) to \( N \)? Wait, no, the diagram: points \( K \), \( N \) on one line, \( M \), \( L \) connected. Wait, the marked angle is at \( L \), between \( LM \) and \( LN \)? Wait, no, the angle is \( \angle MLN \) or \( \angle L \) (if it's the only angle at \( L \) with those sides). Wait, first way: using three points, with the vertex in the middle: \( \angle MLN \). Second way: using the vertex only, if there's only one angle at \( L \) with those sides, so \( \angle L \). Wait, but let's check: the angle is formed by \( LM \) and \( LN \), so vertex \( L \), so one name is \( \angle L \) (if it's the only angle at \( L \) with those two sides), and another is \( \angle MLN \) (or \( \angle NLM \)). Wait, maybe \( \angle MLN \) and \( \angle L \). Wait, let's confirm: in angle naming, we can name it by the vertex (if unique) or by three points (vertex in middle). So the marked angle has vertex \( L \), and sides \( LM \) and \( LN \) (or \( LM \) and \( LK \)? Wait, no, the diagram: \( K \)---\( N \)---\( M \), and \( K \)---\( L \), \( N \)---\( L \), \( M \)---\( L \). So the marked angle is at \( L \), between \( LM \) and \( LN \). So first name: \( \angle MLN \) (three points, vertex \( L \) in middle), second name: \( \angle L \) (since it's the only angle at \( L \) with those two sides). Wait, or maybe \( \angle NLM \) and \( \angle L \). Alternatively, maybe \( \angle MLN \) and \( \angle L \).

Step2: Confirm the names

So two ways: one using three points (vertex in the middle) and one using the vertex. So \( \angle MLN \) and \( \angle L \), or \( \angle NLM \) and \( \angle L \).

Answer:

\( \angle MLN \), \( \angle L \) (or \( \angle NLM \), \( \angle L \))