1. **Stating the problem:** We have a circle divided into 6 equal wedge-shaped sectors, each with a radius of 4 meters. One sector is labeled 45°, and we want to understand the geometry and measurements related to this sector. 2. **Formula and rules:** The circumference of a circle is given by $$C = 2\pi r$$ where $r$ is the radius. 3. **Calculate the circumference:** Given $r = 4$ m, $$C = 2\pi \times 4 = 8\pi \text{ m}$$ 4. **Calculate the arc length of one sector:** Since the circle is divided into 6 equal sectors, each sector's central angle is $$\frac{360^\circ}{6} = 60^\circ$$. 5. **Arc length formula:** $$\text{Arc length} = \frac{\theta}{360^\circ} \times C$$ where $\theta$ is the central angle. 6. **Calculate arc length for 60° sector:** $$\text{Arc length} = \frac{60^\circ}{360^\circ} \times 8\pi = \frac{1}{6} \times 8\pi = \frac{8\pi}{6} = \frac{4\pi}{3} \text{ m}$$ 7. **Regarding the 45° label:** The 45° angle shown is not the central angle of the sector but likely an angle inside the sector or related to a triangle formed within the sector. 8. **Summary:** The radius is 4 m, each sector has a central angle of 60°, and the arc length of each sector is $\frac{4\pi}{3}$ m. The 45° angle is an additional angle inside the sector, possibly for further calculations. **Final answer:** Each sector has an arc length of $\frac{4\pi}{3}$ meters with radius 4 meters and central angle 60°.