Where does the vertex of an angle lie?

Options

A. in its interior
B. in its exterior
C. on the angle
D. done of these

Answer

To determine where the vertex of an angle lies, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of a Vertex**:
- The vertex of an angle is the point where the two rays (or line segments) that form the angle meet.

2. **Visualize the Angle**:
- Draw an angle by creating two rays that start from a common point. Label the point where the rays meet as the vertex (let's call it point A).

3. **Identify the Position of the Vertex**:
- The vertex is located at the point where the two rays meet. This point is not inside the angle (interior) or outside the angle (exterior); it is exactly at the point where the rays intersect.

4. **Analyze the Options**:
- Option A: In its interior - This is incorrect because the vertex is not inside the angle.
- Option B: In its exterior - This is also incorrect because the vertex is not outside the angle.
- Option C: On the angle - This is correct because the vertex is precisely at the point where the two rays meet.
- Option D: None of this - This is incorrect since option C is valid.

5. **Conclusion**:
- The correct answer is Option C: The vertex of an angle lies on the angle.