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

Options

A. `25^@`
B. `33^@`
C. `42^@`
D. `40^@`

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 matches its original position in a full 360-degree rotation.

2. **Identifying the Order**:
- The question states that the figure has a rotational symmetry of order more than 1. This means that when we rotate the figure, it will match its original position at least twice within a full rotation (360 degrees).

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 rotational symmetry.

4. **Factors of 360 Degrees**:
- Since the angle of rotation must be a factor of 360 degrees, we need to find the factors of 360. The factors of 360 degrees include: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, and 360.

5. **Evaluating the Options**:
- Now, we need to evaluate the given options:
- A. 25 degrees
- B. 33 degrees
- C. 42 degrees
- D. 40 degrees
- We check which of these options is a factor of 360:
- 25 is not a factor of 360.
- 33 is not a factor of 360.
- 42 is not a factor of 360.
- 40 is a factor of 360 (since \( 360 \div 40 = 9 \)).

6. **Conclusion**:
- Therefore, the angle of rotation for a figure that has a rotational symmetry of order more than 1 can be 40 degrees. Hence, the correct answer is **D. 40 degrees**.