Which of the following letters has rotational symmetry of order more than 1 but not any line of symmetry?

Options

A. X
B. S
C. B
D. T

Answer

To solve the question of which letter has rotational symmetry of order more than 1 but does not have any line of symmetry, we can follow these steps:

### Step 1: Understand the Concepts
- **Rotational Symmetry**: A shape has rotational symmetry if it can be rotated (less than a full turn) and still look the same. The order of rotational symmetry is the number of times a shape fits onto itself during a full rotation (360 degrees).
- **Line of Symmetry**: A shape has a line of symmetry if it can be divided into two identical halves that are mirror images of each other.

### Step 2: Analyze Each Letter
1. **Letter X**:
- Has two lines of symmetry (vertical and horizontal).
- **Conclusion**: Not our answer.

2. **Letter S**:
- Does not have any line of symmetry.
- When rotated 180 degrees, it looks the same.
- **Conclusion**: Has rotational symmetry of order 2.

3. **Letter B**:
- Has a vertical line of symmetry.
- **Conclusion**: Not our answer.

4. **Letter T**:
- Has a vertical line of symmetry.
- **Conclusion**: Not our answer.

5. **Other Letters (A, C, D)**:
- All have at least one line of symmetry.
- **Conclusion**: Not our answer.

### Step 3: Identify the Correct Answer
- The only letter that has rotational symmetry of order more than 1 (specifically order 2) and does not have any line of symmetry is **S**.

### Final Answer:
The letter **S** has rotational symmetry of order more than 1 but does not have any line of symmetry.

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