see the attached figure with letters to better understand the problem
we know that
m∠BCA=m∠ECD ----------> by vertical angles
m∠BAC=m∠CED --------> given problem
we know that
If two triangles have two identical internal angles, then the triangles are similar.
so
Triangles ABC and EDC are similar
by proportion
[tex]\frac{x}{15} =\frac{8}{5} \\ \\5*x=8*15\\ \\x=(8*15)/5\\ \\x=24\ in[/tex]
therefore
the answer is
the value of x is [tex]24\ in[/tex]
