Angle Egax 1B65E2

1. **State the problem:** We are given a circle with points A, B, C, E, and G on the circumference and a tangent line FED touching the circle at point E. We know angle $\angle ABC = 93^\circ$ and angle $\angle CED = x^\circ$. We need to find the size of angle $\angle EGA$ in terms of $x$ and justify the answer. 2. **Recall important rules:** - The angle between a tangent and a chord through the point of contact equals the angle in the alternate segment of the circle. - This is known as the Alternate Segment Theorem. 3. **Apply the theorem:** Since FED is tangent at E, the angle between the tangent FED and chord EG, which is $\angle CED = x^\circ$, equals the angle in the alternate segment, which is $\angle EGA$. 4. **Conclusion:** Therefore, by the Alternate Segment Theorem, $$\angle EGA = x^\circ.$$