1. **State the problem:** We have a circle with center C and radius 7 m. The central angle $\angle DCE$ measures 100°. We need to find the length of the major arc $dFE$, which is the arc opposite the 100° angle. 2. **Recall the formula for arc length:** The length of an arc $L$ is given by $$L = r \times \theta$$ where $r$ is the radius and $\theta$ is the central angle in radians. 3. **Convert the central angle to radians:** Since the full circle is 360°, the major arc corresponds to the angle $$360^\circ - 100^\circ = 260^\circ$$ Convert 260° to radians: $$\theta = 260^\circ \times \frac{\pi}{180^\circ} = \frac{260\pi}{180} = \frac{13\pi}{9}$$ 4. **Calculate the length of the major arc:** Using the formula: $$L = r \times \theta = 7 \times \frac{13\pi}{9} = \frac{91\pi}{9}$$ 5. **Include the unit:** The length of the major arc $dFE$ is $$\frac{91\pi}{9} \text{ meters}$$ **Final answer:** The length of the major arc $dFE$ is $\frac{91\pi}{9}$ meters.