What is ae ?

enter your answer in the box.

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.

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