Question says to find AE 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+6}{2x+6}=\frac{8}{10} [/tex]
10(x+6)=8(2x+6)
10x+60=16x+48
10x-16x=48-60
-6x=-12
x=2
We have to find AE which is 2x+6
AE= 2x+6 = 2*2+6= 4+6 = 10
Hence final answer is AE = 10.
