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The task is to determine the **number of lines of symmetry** and the **order of rotational symmetry** for each of the three alloy wheels shown (labeled as a, b, and c).

### Explanation of terms:
- **Lines of symmetry**: A line through the center of an object such that when the object is folded along that line, both halves match perfectly.
- **Rotational symmetry**: The number of positions in which an object looks exactly the same during a full 360-degree rotation.

### Analyzing the wheels:

#### a) Wheel a:
- **Lines of symmetry**: This wheel has 6 identical spokes. Each spoke, and the spaces between, create mirror images along axes passing through the center and between each pair of adjacent spokes. Therefore, there are **6 lines of symmetry**.
- **Rotational symmetry**: Since the wheel looks the same after a rotation of \( \frac{360^\circ}{6} = 60^\circ \), the order of rotational symmetry is **6**.

#### b) Wheel b:
- **Lines of symmetry**: This wheel has 7 spokes. Since all spokes are identical, it has **7 lines of symmetry** (one line for each spoke).
- **Rotational symmetry**: The wheel will look the same after each \( \frac{360^\circ}{7} \approx 51.43^\circ \) rotation. Hence, the order of rotational symmetry is **7**.

#### c) Wheel c:
- **Lines of symmetry**: This wheel has 5 spokes, but the pattern of the spokes is not completely symmetric. Thus, it seems to have **5 lines of symmetry**.
- **Rotational symmetry**: The wheel will look the same after each \( \frac{360^\circ}{5} = 72^\circ \) rotation, giving it an order of rotational symmetry of **5**.

### Summary:
- **Wheel a**: 6 lines of symmetry, order of rotational symmetry 6.
- **Wheel b**: 7 lines of symmetry, order of rotational symmetry 7.
- **Wheel c**: 5 lines of symmetry, order of rotational symmetry 5.

Would you like more details or further explanation?

Here are 5 related questions to explore:
1. How do you determine the order of rotational symmetry for irregular shapes?
2. Can an object have rotational symmetry without having lines of symmetry?
3. What is the significance of symmetry in design and engineering?
4. How can rotational symmetry be used in architecture and construction?
5. What are some real-world applications of symmetry in vehicle design?

**Tip:** For any regular polygon (like a hexagon or pentagon), the number of sides is equal to both the lines of symmetry and the order of rotational symmetry.

Ignoring the wheel nuts, find the number of lines of symmetry and order of rotational symmetry for each wheel.

Explore how to determine the lines of symmetry and the order of rotational symmetry in car alloy wheels. This problem covers key geometry concepts, ideal for students in Grades 6-8.

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