Answer:
The value of x is 24.
Step-by-step explanation:
In triangle ABC and EDC,
[tex]\angle A=\angle E[/tex] (Given)
[tex]\angle ACB=\angle ECD[/tex] (vertically opposite angles)
By AA property of similarity,
[tex]\triangle ABC\sim \triangle EDC[/tex]
The corresponding sides of similar triangles are proportional.
[tex]\frac{AB}{BC}=\frac{ED}{DC}[/tex]
[tex]\frac{5}{8}=\frac{15}{x}[/tex]
[tex]5x=15\times 8[/tex]
Divide both sides by 5.
[tex]x=3\times 8[/tex]
[tex]x=24[/tex]
Therefore the value of x is 24.
