Question

In fig 34bthe side BC of triangle ABC is produced to form ray BD.Ray CE is drawn parallel to BA.Show directly without AMS that Angle ACD= anglenA+anglenB and deduce angle A+angle B + angle C=180°​

Answer 1

Answer:

From the figure we know that ∠ACB and ∠ACD form a linear pair of angles

So we get

∠ACB+∠ACD=180

∘

By substituting the values

∠ACB+128

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=180

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On further calculation

∠ACB=180

∘

−128

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By subtraction

∠ACB=52

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We know that the sum of all the angles in a triangle is 180

∘

.

So we can write it as

∠ABC+∠ACB+∠BAC=180

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By substituting the values

43

∘

+52

∘

+∠BAC=180

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On further calculation

∠BAC180

∘

−43

∘

−52

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By subtraction

∠BAC=180

∘

−95

∘

∠BAC=85

∘

Therefore, ∠BAC=85

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and ∠ACB=52

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Step-by-step explanation:

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