To answer this question we will use the following diagram as reference:
Given that angles B and D are perpendiculars, l and m are parallel, therefore angles C and D have to be equal given that they are alternate interior angles.
Therefore, by the AAA criteria, the given triangles are similar.
Now, since the triangles are similar, we know that:
[tex]\frac{2}{5}=\frac{x}{7.5}\text{.}[/tex]
Multiplying the above equation by 7.5, we get:
[tex]\frac{2}{5}\times7.5=\frac{x}{7.5}\times7.5.[/tex]
Finally, simplifying the above result, we get:
[tex]3=x\text{.}[/tex]
Answer:
[tex]x=3.[/tex]
