A figure has a rotational symmetry of order more than 1, the angle of rotation can be

Options

A. `21^@`
B. `22^@`
C. `23^@`
D. `24^@`

Answer

To solve the question regarding the angle of rotation for a figure with a rotational symmetry of order more than 1, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Rotational Symmetry**:
- A figure has rotational symmetry if it can be rotated around a central point and still look the same at certain angles. The order of rotational symmetry refers to how many times the figure looks the same in one complete turn (360 degrees).

2. **Identifying the Order**:
- If a figure has a rotational symmetry of order more than 1, it means that there are multiple angles at which the figure can be rotated and still appear unchanged.

3. **Calculating the Angle of Rotation**:
- The angle of rotation can be calculated using the formula:
\[ \text{Angle of rotation} = \frac{360^\circ}{n} \]
where \( n \) is the order of symmetry.

4. **Determining Possible Values**:
- Since the order is more than 1, \( n \) can be any integer greater than 1 (e.g., 2, 3, 4, 5, etc.).
- The angle of rotation will thus be:
- For \( n = 2 \): \( \frac{360^\circ}{2} = 180^\circ \)
- For \( n = 3 \): \( \frac{360^\circ}{3} = 120^\circ \)
- For \( n = 4 \): \( \frac{360^\circ}{4} = 90^\circ \)
- For \( n = 5 \): \( \frac{360^\circ}{5} = 72^\circ \)
- And so on.

5. **Conclusion**:
- The angle of rotation can be any divisor of 360 degrees that corresponds to an integer greater than 1. Therefore, the possible angles of rotation can be 180°, 120°, 90°, 72°, etc.