Question

The sides AB, BC and CA of a ∆ABC are produced in order to form exterior angles <CEF, <ACD and <BAE. The sum of these exterior angles is:--​

Answer 1

Answer:

ABC+∠CBF=180

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∠ACB+∠ACD=180

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∠BAC+∠BAE=180

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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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Step-by-step explanation:

Sides BC, CA and AB of a triangle ABC are produced in order, forming exterior angles ∠ACD, ∠BAE, and∠CBF. Show that ∠ACD + ∠BAE + ∠CBF = 360°.Read more on Sarthaks.com - https://www.sarthaks.com/680232/sides-bc-and-triangle-abc-are-produced-in-order-forming-exterior-angles-acd-bae-andcbf

Answer 2

$angle \: l \: + \: angle \: b \: = \: angle \: acd \: = > \: 1 \\ angle \: 3 \: + \: angle \: 2 \: = \: angle \: bae \: = > \: 2 \\ angle \: 3 \: + \: angle \: 1 \: = \: angle \: cbf \: = > \: 3 \\ from \: 1 \: 2 \: 3 \\ angle \: 1 \: + \: angle \: 2 \: + \: angle \: 3 \: + \: angle \: 2 \: + \: angle \: 3 \: + \: angle \: 1 \: \\ = \: angle \: acd \: + \: angle \: bae \: + \: angle \: cbf \\ 2(angle \: 1 \: + \: angle \: 2 \: + angle \: 3) = angle \: acd \: + angle \: bae \: + \: angle \: cbf \\ 2 \times 190 = angle \: acd \: + \: angle \: baf \: + \: angle \: cbf \\ 360degree \: = \: angle \: acd \: + \: angle \: bae \: + \: angle \: cbf.$