https://r2.erweima.ai/mathbot/image/17259213097110sn74zg3.jpg

The problem asks to name the vertex and sides of the angle formed by the points \( I \), \( J \), and \( K \) in the diagram. 

Let's analyze the diagram and the options provided:

- In the image, \( J \) is the point where two rays meet, so it is the vertex of the angle.
- The sides of the angle are the rays extending from \( J \), which are \( \overrightarrow{JK} \) and \( \overrightarrow{JI} \).
  - \( \overrightarrow{JK} \) is the ray going towards point \( K \).
  - \( \overrightarrow{JI} \) is the ray going towards point \( I \).

Now let's check the options:

- **Option A**: Vertex = \( J \), Sides = \( \overrightarrow{JK} \) and \( \overrightarrow{JI} \).  
  This matches the correct configuration.
  
- **Option B**: Vertex = \( I \), Sides = \( \overrightarrow{IJ} \) and \( \overrightarrow{IK} \).  
  This is incorrect because the vertex is \( J \), not \( I \).
  
- **Option C**: Vertex = \( I \), Sides = \( \overrightarrow{JK} \) and \( \overrightarrow{JI} \).  
  This is incorrect because the vertex is \( J \), not \( I \).

- **Option D**: Vertex = \( K \), Sides = \( \overrightarrow{JK} \) and \( \overrightarrow{JI} \).  
  This is incorrect because the vertex is \( J \), not \( K \).

- **Option E**: Vertex = \( J \), Sides = \( \overrightarrow{JK} \) and \( \overrightarrow{KI} \).  
  This is incorrect because the second side is \( \overrightarrow{JI} \), not \( \overrightarrow{KI} \).

The correct answer is **Option A**: Vertex = \( J \), Sides = \( \overrightarrow{JK} \) and \( \overrightarrow{JI} \).

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Would you like more details on any part of the solution? Here are five related questions you can explore:

1. What are the properties of angles formed by two rays with a common endpoint?
2. How can you identify the vertex of an angle in a geometric diagram?
3. What is the difference between a ray and a line segment in geometry?
4. How do you name an angle when given three points?
5. How do you measure an angle using a protractor?

**Tip:** When naming an angle, always place the vertex point in the middle when using three letters (e.g., \( \angle JIK \)).

Name the vertex and sides of each angle based on the points I, J, and K.

Learn how to identify the vertex and sides of an angle using points I, J, and K. This problem covers basic geometric concepts and is suitable for students in Grades 6-8.

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