Question

What is ED ? Enter your answer in the box. units

Answer 1

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:

$\frac{DE}{AE}=\frac{CD}{BA}$

$=\frac{x+4}{2x+4}=\frac{6}{9}$

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.

Answer 2

X is 4
so ED is 4 + 4
= 8