We know the angles in a triangle sum to 180 degrees. Thus, we can write:
[tex]\angle1+\angle2+\angle3=180[/tex]Also, we know straight line is 180 degrees. Thus we can write:
[tex]\angle1+\angle4=180[/tex]Putting these 2 equations together, we have:
[tex]\begin{gathered} 180=180 \\ \angle1+\angle2+\angle3=\angle1+\angle4 \\ \therefore\angle2+\angle3=\angle4 \end{gathered}[/tex]Now, we substitute the known expressions for the angles and solve for x:
[tex]\begin{gathered} \angle2+\angle3=\angle4 \\ \frac{4}{3}x+20=2x \\ 2x-\frac{4}{3}x=20 \\ \frac{2}{3}x=20 \\ x=\frac{20}{\frac{2}{3}} \\ x=20\times\frac{3}{2} \\ x=30 \end{gathered}[/tex]