Question

two parallel vertical lines (with arrows) are cut by a transversal. angles labeled ( 4x^circ ) and ( x^circ ) are formed at the intersection with the right vertical line.

Explanation:

Step1: Identify angle relationship

The two angles \(4x^\circ\) and \(x^\circ\) are supplementary (they form a linear pair), so their sum is \(180^\circ\).
\[4x + x = 180\]

Step2: Solve for \(x\)

Combine like terms:
\[5x = 180\]
Divide both sides by 5:
\[x=\frac{180}{5}=36\]

Answer:

\(x = 36\)