Question

32. The sides BC, CA & AB of a triangle ABC, are produced in order, forming exterior angles ZACD,
ZBAE & ZCBF, show that : ZACD + ZBAE + ZCBF = 360°.
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Answer 1

Answer:

∠ABC+∠CBF=180

∘

[Linear pair]………..(i)

∠ACB+∠ACD=180

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[Linear pair]……(ii)

∠BAC+∠BAE=180

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[Linear pair]…….(iii)

Byadding(i), (ii) and (iii)

∠ABC+∠CBF+∠ACB+∠ACD+∠BAC+∠BAE=180+180+180

∠ABC+∠ACB+∠BAC+∠CBF+∠ACD+∠BAE=540

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180+∠CBF+∠ACD+∠BAE=540

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[Sum of the angles of a triangle 180

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]

∠CBF+∠ACD+∠BAE=360

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solution