Answer 1

Given: `∠ ADE = ∠ ABC`

To find: The value of CE

Since `∠ ADE = ∠ ABC`  

∴ DE || BC       (Two lines are parallel if the corresponding angles formed are equal)

According to basic proportionality theorem if a line is parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.

In ∆ABC, DE || BC

`(AD)/(DB)=(AE)/(EC)`

`2/3=3/EC`

`EC=(3xx3)/2`

`EC =9/2`

Hence we got the result `C`