In the image, the question asks how the given angle can be named, using a geometric diagram with three labeled points: $A$, $B$, and $C$.

Analyzing the diagram:

• The angle in question is $\angle ABC$, where point $B$ is the vertex of the angle.
• The ray $BA$ and the ray $BC$ form the angle, making $B$ the vertex, and $A$ and $C$ are points on the rays.

Naming conventions for angles:

1. $\angle B$: The angle can be named by its vertex alone, which is $B$.
2. $\angle ABC$: The angle can be named using three points, where $B$ is the vertex, and the other two letters $A$ and $C$ define the rays forming the angle. In this case, $\angle ABC$ is correct.
3. $\angle CBA$: This is also a valid way to name the angle, since it just reverses the order of points, but still keeps $B$ as the vertex.

Valid names for the angle:

• $\angle ABC$
• $\angle CBA$

Conclusion:

You should select:

• $\angle ABC$
• $\angle CBA$

Would you like more detailed explanations on angles or have any questions about this?

Here are 5 questions to deepen understanding:

1. What does the vertex of an angle represent?
2. Can an angle be named using only two points? Why or why not?
3. What are some other examples of how angles are labeled in geometry?
4. Why is the order of points important when naming an angle?
5. Can an angle have more than one valid name? If yes, why?

Tip: Always start and end angle names with points on the rays, and ensure the vertex is in the middle.