Let the measure of angle 2 be given as [tex]\( 92^\circ \)[/tex].
The measure of angle 4 is given as [tex]\( \left(\frac{1}{2} x\right)^\circ \)[/tex].
We are to find the value of [tex]\( x \)[/tex] such that angle 2 equals angle 4.
Set up an equation to represent this relationship:
[tex]\[ 92 = \left(\frac{1}{2} x\right) \][/tex]
To solve for [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex]. We do this by eliminating the fraction [tex]\(\frac{1}{2}\)[/tex] on the right-hand side. Multiply both sides of the equation by 2:
[tex]\[ 2 \cdot 92 = 2 \cdot \left(\frac{1}{2} x\right) \][/tex]
This simplifies to:
[tex]\[ 184 = x \][/tex]
Therefore, the value of [tex]\( x \)[/tex] is:
[tex]\[ \boxed{184} \][/tex]
