Respuesta :

the two lines are parallel, the angle they make should be equal and one angle is common so the triangles are similar by AAA.

Now the ratio of sides are [tex] \frac{20+8}{20}=\frac{x+18}{x}[/tex]

use divideno, [tex]\frac8{20}=\frac{18}x[/tex]

and then inverse the whole equation to get [tex]x=20\times\frac{18}{8} \implies x= 45[/tex]

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Answer:

[tex]\Large \boxed{\mathrm{B) \ 45}}[/tex]

Step-by-step explanation:

We can solve the problem using ratios.

[tex]\displaystyle \frac{x}{20} =\frac{x+18}{20+8}[/tex]

Cross multiply.

[tex]20(x+18)=x(20+8)[/tex]

Expand brackets.

[tex]20x+360=28x[/tex]

Subtract 20x from both sides.

[tex]360=8x[/tex]

Divide both sides by 8.

[tex]45=x[/tex]

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