Proving AB=2CE with AC parallel to DE

[rushikesh]

In the figure attached, I have to prove AB=2CE given that: line AC is parallel to DE and angles as mentioned in the figure. Can anyone please help me to prove the same?

 

[szynkasz]

Calculate angles of the triangle $CDE$ in terms of $\angle BAC$ Then use the sine formula to relate $|CE|$ to $|CD|$

 

[rushikesh]

∠BAC can vary and so will the angles of the Triangle CDE

 

[Nugatory]

∠BAC can vary and so will the angles of the Triangle CDE

They can. But they're related, so you can express one in terms of the other.