Equal Angles

$\mathrm{FEG}$ is an isoceles triangle, so $\angle \mathrm{FEG}=\angle \mathrm{FGE}$.
$\angle \mathrm{FGE}$ and $\angle \mathrm{CEG}$ are equal as they are alternate angles.
Therefore $\angle \mathrm{FEG}=\angle \mathrm{CEG}$.

Further Reading:

Alternate Angles

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