Question

two parallel lines are cut by a transversal, forming adjacent angles ((x - 20)^circ) and (x^circ).

Explanation:

Step1: Identify supplementary angles

The two angles \((x - 20)^\circ\) and \(x^\circ\) are supplementary (they form a linear pair), so their sum is \(180^\circ\).
\[
(x - 20) + x = 180
\]

Step2: Solve for \(x\)

Combine like terms:
\[
2x - 20 = 180
\]
Add 20 to both sides:
\[
2x = 180 + 20
\]
\[
2x = 200
\]
Divide both sides by 2:
\[
x = \frac{200}{2}
\]
\[
x = 100
\]

Answer:

\(x = 100\)