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Answer: the correct answer rho this question is option(c) National Development
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the side of BC of triangle ABC is produced to D If the bisector of angle A meets BC in E. prove that angle abc + angle acd = 2 angle AEC.
Solution :
the bisector of angle A meets BC in E
=> ∠BAE = ∠CAE = x
Let say ∠ABC = ∠ABE = α ( as E is on BC)
∠AEC = ∠ABE + ∠BAE
=> ∠AEC = α + x
∠ACD = ∠AEC + ∠CAE
=> ∠ACD = α + x + x
∠ABC + ∠ACD = α + α + x + x
=> ∠ABC + ∠ACD = 2 ( α + x)
=> ∠ABC + ∠ACD = 2∠AEC
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