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