We can draw the following picture:
From the figure, we can see that triangles ABC and EDC are similar.
Reasons:
By means of AAA (angle-angle-angle) theorem those triangles are similar, that is
they both triangles have the same angles (red, blue, green).
Since both triangles are similar the following ratio must be preserved:
[tex]\frac{60}{2y}=\frac{3x+10}{y}[/tex]
Now, from this ratio, we must find x.
If we move 2y to the right hand side, we get
[tex]60=2y(\frac{3x+10}{y})[/tex]
so we can eliminate y in both, the denominator and numerator. Then, we obtain
[tex]60=2(3x+10)[/tex]
which is equal to
[tex]60=6x+20[/tex]
If we move 20 to the left hand side as -20, we get
[tex]\begin{gathered} 60-20=6x \\ 40=6x \end{gathered}[/tex]
then, we have
[tex]\begin{gathered} x=\frac{40}{6} \\ x=\frac{20}{3} \end{gathered}[/tex]
Therefore, x is equal to 20/3.
