Question

What is AE ? Enter your answer in the box. units wo segments A D and B C intersect at point E to form two triangles A B E and D C E. Side A B is parallel to side D C. A E is labeled 2 x plus 6. E D is labeled x plus 6. A B is 10 units long. D C is 8 units long.

Answer 1

According to question

AD is parallel to CD

Thus in triangle ABE  and CDE

Angle BAE = Angle EDC  
Angle ABE =  Angle ECD
Also
Angle AEB =  Angle CED
Thus
the triangles are similar

Thus      AE =  ED
2x+6 = x + 6
x =0
Thus AE = 2x + 6
AE = 6