Which one of the following statements is true?

Options

A. An angle has two lines of symmetry
B. A regular hexagon has only 4 lines of symmetry
C. A regular polygon of 10 sides has 10 lines of symmetry
D. A ccircle has no line of symmetry

Answer

To determine which statement is true, we will analyze each of the given statements regarding lines of symmetry in angles, polygons, and circles.

### Step-by-Step Solution

1. **Understanding Lines of Symmetry**:
- A line of symmetry is a line that divides a shape into two identical parts that are mirror images of each other.

2. **Analyzing the First Statement**:
- The first statement claims that an angle has two lines of symmetry.
- To test this, consider an angle (for example, a 60-degree angle).
- If we draw a line of symmetry through the vertex and the midpoint of the opposite side, we can see that this line divides the angle into two equal parts.
- However, there is only one line of symmetry for any given angle, not two.
- Therefore, this statement is **false**.

3. **Analyzing the Second Statement**:
- The second statement suggests that in a regular polygon, the number of lines of symmetry is equal to the number of sides.
- For example, a square (which is a regular polygon) has 4 sides and 4 lines of symmetry (two diagonals and two lines through the midpoints of opposite sides).
- This statement is **true** for all regular polygons.

4. **Analyzing the Third Statement**:
- The third statement claims that a circle has no lines of symmetry.
- This is incorrect because a circle has an infinite number of lines of symmetry. Any diameter of the circle acts as a line of symmetry, dividing the circle into two equal halves.
- Therefore, this statement is **false**.

5. **Conclusion**:
- After analyzing all three statements, we find that the second statement is true: "In a regular polygon, the number of lines of symmetry is equal to the number of sides."

### Summary of Findings:
- **First Statement**: False (an angle has only one line of symmetry).
- **Second Statement**: True (in a regular polygon, the number of lines of symmetry equals the number of sides).
- **Third Statement**: False (a circle has infinite lines of symmetry).

### Final Answer:
The true statement is: "In a regular polygon, the number of lines of symmetry is equal to the number of sides."