Given DEC = 28^.
This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
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 $\angle EGC$.
$$ \angle CEG = 180^\circ - (\angle EGC + \angle ECG) $$
$$ \angle CEG = 180^\circ - (32^\
