Question

In figure, if AD = 6 cm, DB = 9 cm, AE = 8 cm and EC = 12 cm and ∠ADE = 48°. Find ∠ABC. 

Answer 1

Given: AD = 6 cm, DB = 9 cm

AE = 8 cm, EC = 12 cm, ∠ADE = 48°

To find: ΔABC = ?

Proof: In ΔABC

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

`6/9 = 8/12`

`2/3 = 2/3`

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

DE || BC   ...(Converse of BPT)

∠ADE = ∠ABC   ...(Corresponding angles)

So, ∠ABC = 48°