What is ae ?

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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:

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.

where's the diagram?

step-by-step explanation: