What is the smallest angle of rotational symmetry for a square? \( 45^{\circ} \) \( 90^{\circ} \) \( 180^{\circ} \) \( 360^{\circ} \)

The **smallest angle of rotational symmetry** for a square is **\(90^{\circ}\)**. ### Explanation: A shape has rotational symmetry if it can be rotated (less than a full turn) about its center and still look the same as it did before the rotation. For a **square**: - **\(90^{\circ}\)** rotation: The square maps onto itself. Each side moves to the position of the next side. - **\(180^{\circ}\)** rotation: The square still maps onto itself, but it's not the smallest possible angle. - **\(270^{\circ}\)** rotation: Similar to \(90^{\circ}\), but larger. - **\(360^{\circ}\)** rotation: Completes a full turn, bringing the square back to its original position, but it's not the smallest angle. Rotating a square by **\(45^{\circ}\)** does **not** map the square onto itself. Instead, the vertices of the square move to the midpoints of the original sides, changing its appearance. Therefore, the smallest angle that allows the square to map onto itself through rotation is **\(90^{\circ}\)**. **Answer:** \(90^{\circ}\)