The diagram shows three points $K$, $L$, and $M$, connected by lines, forming angles at point $L$. Based on the geometric configuration and the labeled points, we can determine which angle names are valid.

Naming angles:

• The middle letter of an angle name indicates the vertex where the angle is located.
• Therefore, any valid angle must have point $L$ as the middle letter, as $L$ is where the two lines meet to form angles.

Valid angle names:

• $\angle KLM$ (the angle formed by points $K$, $L$, and $M$)
• $\angle MLK$ (the same angle as $\angle KLM$ but named in reverse order)

The other names are not valid because:

• They either do not have $L$ as the vertex (e.g., $\angle K$, $\angle M$).
• They list points in an order that does not form an angle based on the diagram (e.g., $\angle MKL$, $\angle LMK$).

Therefore, the valid angle names are:

• $\angle KLM$
• $\angle MLK$

Let me know if you'd like more details or have any further questions!

Here are five related questions to expand on this:

1. How can you determine the vertex of an angle from a given angle name?
2. Why are some angle names considered invalid in this context?
3. How can we distinguish between different angles at a single point when more lines are present?
4. What is the significance of reversing the order of points in angle naming (e.g., $\angle KLM$ vs. $\angle MLK$)?
5. How can you calculate the measure of an angle if you know the positions of the points?

Tip: When naming an angle, always ensure the vertex is the middle point in the three-letter name.