∠2 and ∠3 are alternate interior angles. In order to A II B, the alternate interior angles must be equal.
Then,
[tex]\begin{gathered} \angle2=\operatorname{\angle}3 \\ 3x-10=x+30 \end{gathered}[/tex]
To find x, subtract x from both sides of the equation:
[tex]\begin{gathered} 3x-10-x=x+30-x \\ 3x-x-10=x-x+30 \\ 2x-10=30 \end{gathered}[/tex]
Now, add 10 to both sides of the equation:
[tex]\begin{gathered} 2x-10+10=30+10 \\ 2x=40 \end{gathered}[/tex]
Finally, divide both sides by 2:
[tex]\begin{gathered} \frac{2x}{2}=\frac{40}{2} \\ x=20 \end{gathered}[/tex]
Answer: x = 20.
