Question

note: angles not necessarily drawn to scale.

$x = square$

Explanation:

Step1: Find the measure of ∠DEB

∠DEB is given as \(20^{\circ}\).

Step2: Use the property of vertical angles

Since \(AB\) is a straight line, the sum of angles around point \(E\) on one side of \(AB\) is \(180^{\circ}\). But we can also use the property that \(∠CEG\) (which is \(x^{\circ}\)) and \(∠DEB\) are related through the angle \(∠FED = 80^{\circ}\).
We know that \(x+80 = 20 + 180 - 180+ 80\) (alternatively, using the fact that \(x = 20\) (because of the vertical - angle - like relationship considering the straight - line and angle - sum properties. Another way:
Since \(AB\) is a straight line, and if we consider the angles around point \(E\) for the non - straight - line part. But more simply, note that \(x\) and the angle composed of \(20^{\circ}\) (because of the parallel - line - like (assuming some implicit parallelism from the problem's structure, or more accurately, using the angle - equality based on the geometric configuration where \(x\) and \(20^{\circ}\) are equal due to the way the lines are arranged (if we assume \(CD\parallel AB\) (implicit from the problem's need to find \(x\) in this simple form)).

Answer:

\(20\)