1. **State the problem:** We need to find the size of angle $EFG$ in a cyclic quadrilateral $EFGD$ inscribed in a circle, given that angle $D$ is $62^\circ$ and angle $EFG$ is $118^\circ$. 2. **Recall the property of cyclic quadrilaterals:** Opposite angles in a cyclic quadrilateral sum to $180^\circ$. That is, if $EFGD$ is cyclic, then: $$\angle EFG + \angle EDG = 180^\circ$$ 3. **Identify the opposite angle to $EFG$:** The angle opposite to $EFG$ is angle $EDG$ (angle at point $D$), which is given as $62^\circ$. 4. **Apply the property:** $$\angle EFG + 62^\circ = 180^\circ$$ 5. **Solve for $\angle EFG$:** $$\angle EFG = 180^\circ - 62^\circ = 118^\circ$$ 6. **Conclusion:** The size of angle $EFG$ is $118^\circ$, which matches the given value, confirming the property of cyclic quadrilaterals. **Reason:** Opposite angles in a cyclic quadrilateral sum to $180^\circ$.