Question

which angle number represents an angle vertical to ∠cgb?

Explanation:

Step1: Recall the definition of vertical angles

Vertical angles are a pair of non - adjacent angles formed by the intersection of two lines. They are opposite each other.

Step2: Identify the vertical angle to \(\angle CGB\)

Looking at the intersection of lines \(CD\) and \(AB\) at point \(G\), the angle opposite to \(\angle CGB\) (which is \(\angle 2\)) is \(\angle 5\) (formed by the intersection of lines \(CD\) and \(EF\) at point \(H\) is not relevant here. Focusing on the intersection at \(G\), when two lines intersect, vertical angles are formed. \(\angle CGB\) and \(\angle AGD\) (\(\angle 5\) is not correct. Wait, no, re - check. Wait, lines \(AB\) and \(CD\) intersect at \(G\). \(\angle CGB\) and \(\angle AGD\) are vertical angles. But in the numbering, \(\angle CGB=\angle 2\), and its vertical angle is \(\angle 5\) (no, wrong. Wait, no. Wait, two lines \(AB\) and \(CD\) intersect. \(\angle 1\) and \(\angle 3\) are vertical, \(\angle 2\) (\(\angle CGB\)) and \(\angle AGD\) (which is \(\angle 5\) if we consider the numbering. Wait, no, actually, when two lines \(AB\) and \(CD\) intersect:
\(\angle CGB\) (\(\angle 2\)) and \(\angle AGD\) (assuming \(\angle AGD\) is labeled as \(\angle 5\) in the standard vertical - angle formation. Wait, no, actually, vertical angles: if two lines intersect, say line \(l_1\) and \(l_2\). The pairs of vertical angles are: if \(\angle x\) is formed, then the angle opposite to \(\angle x\) (not adjacent) is its vertical angle. In the given figure, for \(\angle CGB\) (let's assume it's \(\angle 2\)), its vertical angle is \(\angle AGD\) (which is \(\angle 5\) in the numbering of the problem's figure.

Answer:

\(\angle 5\)