Solution:
Given:
[tex]\begin{gathered} \angle2=3x-20 \\ \angle5=x+20 \end{gathered}[/tex]
For line A and line B to be parallel lines, then the measure of angle 2 must be equal (congruent) to the measure of angle 5.
Thus,
[tex]\angle2\cong\angle5[/tex]
If angle 2 and angle 5 are congruent, then A || B.
Angle 2 and angle 5 are corresponding angles when A || B.
Corresponding angles are formed when a transversal passes through two lines. The angles that are formed in the same position, in terms of the transversal, are corresponding angles. Corresponding angles are congruent.
Hence,
[tex]\begin{gathered} \angle2=\angle5\ldots\ldots\ldots\ldots\ldots\text{.Corresponding angles are congruent} \\ 3x-20=x+20 \\ \text{Collecting the like terms to solve for x,} \\ 3x-x=20+20 \\ 2x=40 \\ \text{Dividing both sides by 2,} \\ x=\frac{40}{2} \\ x=20 \end{gathered}[/tex]
Therefore, the value of x that makes A || B is 20
