Given DEC = 28^.

Step 1: Calculate $\angle ECG$.
Since line DE is parallel to line CG, and CE is a transversal, the alternate interior angles are equal.

$$\angle ECG = \angle DEC$$

Given $\angle DEC = 28^\circ$.

$$\angle ECG = 28^\circ$$

Step 2: Calculate $\angle CEG$.
Consider $\triangle CEG$. The sum of angles in a triangle is $180^\circ$.
We are given $\angle AGE = 32^\circ$, which is $\angle EGC$.

$$\angle CEG = 180^\circ - (\angle EGC + \angle ECG)$$ $$$$