Question

what is an angle that is supplementary to \\( \angle egf \\)?

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\).

Step2: Identify the angle adjacent to \(\angle EGF\) that forms a linear pair

A linear pair of angles is supplementary. The angle adjacent to \(\angle EGF\) that forms a linear pair is \(\angle FGE\)'s adjacent angle. Looking at the diagram, \(\angle EGC\) forms a linear pair with \(\angle EGF\) (since they are adjacent and their non - common sides form a straight line).

Answer:

\(\angle EGC\)