If a regular polygon has n sides, then its number of symmetrical lines is

Options

A. 2
B. 4
C. n
D. n+2

Answer

To determine the number of lines of symmetry in a regular polygon with \( n \) sides, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Regular Polygons**: A regular polygon is a polygon with all sides and angles equal. Examples include equilateral triangles, squares, and regular pentagons.

2. **Identifying Symmetry**: A line of symmetry is a line that divides a shape into two identical parts that are mirror images of each other.

3. **Counting Lines of Symmetry**:
- For a regular polygon with \( n \) sides, there are two types of lines of symmetry:
- Lines that pass through a vertex and the midpoint of the opposite side.
- Lines that pass through the midpoints of two opposite sides.

4. **Total Lines of Symmetry**:
- In a regular polygon with \( n \) sides, there are exactly \( n \) lines of symmetry. This is because:
- Each vertex can be connected to the midpoint of the opposite side, giving \( n \) lines.
- Additionally, if \( n \) is even, there are lines that can connect midpoints of opposite sides, but these are already counted in the \( n \) lines.

5. **Conclusion**: Therefore, the number of lines of symmetry in a regular polygon with \( n \) sides is \( n \).

### Final Answer:
The number of symmetrical lines in a regular polygon with \( n \) sides is \( n \).

---