Question

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

Answer 1

Given AD = 6cm, DB = 9cm

AE = 8cm and EC = 12cm, ∠ADE = 48°

To find:- ∠ABC = ?

Proof:

In ΔABC

`("AD")/("DB") = 6/9 = 2/3`    ...(1)

`("AE")/("EC") = 8/12 = 2/3`   ...(2)

From (1) and (2)

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

DE || BC  ...(Converse of BPT]

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

`\implies` ∠ABC = 48°