Geometry worksheet featuring six different shapes where students must determine if rotational symmetry exists and calculate the angle.

To determine if a figure has rotational symmetry and to find the angle of rotation, we need to check if the figure looks the same after being rotated by a certain angle. The smallest angle of rotation that makes the figure look identical to its original position is called the angle of rotational symmetry.

Let's analyze each figure step by step:

---

1. Rectangle

- Shape: A rectangle.
- Analysis: A rectangle can be rotated by 180° and it will look the same. However, it does not look the same when rotated by 90° or any other smaller angle.
- Conclusion: Yes, it has rotational symmetry.
- Angle of rotation: 180°

---

2. Star (5-pointed)

- Shape: A 5-pointed star.
- Analysis: A 5-pointed star can be rotated by \( \frac{360^\circ}{5} = 72^\circ \) and it will look the same. This is because it has 5 points of symmetry.
- Conclusion: Yes, it has rotational symmetry.
- Angle of rotation: 72°

---

3. Heart

- Shape: A heart.
- Analysis: A heart does not look the same after any rotation less than 360°. Rotating it by any angle will change its appearance.
- Conclusion: No, it does not have rotational symmetry.
- Angle of rotation: N/A

---

4. Cross

- Shape: A cross with equal arms.
- Analysis: This cross can be rotated by 90° and it will look the same. It also looks the same after 180° and 270° rotations.
- Conclusion: Yes, it has rotational symmetry.
- Angle of rotation: 90°

---

5. Triangle (Equilateral)

- Shape: An equilateral triangle.
- Analysis: An equilateral triangle can be rotated by \( \frac{360^\circ}{3} = 120^\circ \) and it will look the same. This is because it has 3 points of symmetry.
- Conclusion: Yes, it has rotational symmetry.
- Angle of rotation: 120°

---

6. Arrow

- Shape: An arrow.
- Analysis: An arrow does not look the same after any rotation less than 360°. Rotating it by any angle will change its direction and appearance.
- Conclusion: No, it does not have rotational symmetry.
- Angle of rotation: N/A

---

Final Answers

1. Rectangle:
- Yes
- Angle of rotation: 180°

2. Star:
- Yes
- Angle of rotation: 72°

3. Heart:
- No
- Angle of rotation: N/A

4. Cross:
- Yes
- Angle of rotation: 90°

5. Triangle:
- Yes
- Angle of rotation: 120°

6. Arrow:
- No
- Angle of rotation: N/A

---

Boxed Final Answer

\[
\boxed{
\begin{array}{ll}
\text{Rectangle:} & \text{Yes, 180°} \\
\text{Star:} & \text{Yes, 72°} \\
\text{Heart:} & \text{No, N/A} \\
\text{Cross:} & \text{Yes, 90°} \\
\text{Triangle:} & \text{Yes, 120°} \\
\text{Arrow:} & \text{No, N/A} \\
\end{array}
}
\]