Question says to find ED based on given information in the picture.
We see that AB and CD are parallel lines
AD acts as transversal on AB and CD
then
∠CDE= ∠BAE {alternate interior angles}
similarly
∠DCE= ∠ABE {alternate interior angles}
∠CED= ∠BEA {opposite angles}
so by AAA property of triangles.
Triangle CDE and triangle BAE are similar.
By properties of similar triangles, we know that ratio of corresponding sides is always equal so we can write:
[tex] \frac{DE}{AE}=\frac{CD}{BA} [/tex]
[tex] =\frac{x+4}{2x+4}=\frac{6}{9} [/tex]
9(x+4)=6(2x+4)
9x+36=12x+24
9x-12x=24-36
-3x=-12
x=4
We have to find AD which is x+4
ED= x+4 = 4+4 = 8
Hence final answer is ED = 8.
