Question

side BC of angleABC has been produced to D on left and to E on right hand side of BC such that​

Answer 1

From the figure we know that ∠DBA and ∠ABC form a linear pair of angles

So we get

∠DBA+∠ABC=180

∘

By substituting the values

106

∘

+∠ABC=180

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On further calculation

∠ABC=180

∘

−106

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By subtraction

∠ABC=74

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

So we get

∠ACB+∠ACE=180

∘

By substituting the values

∠ACB+118

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=180

∘

On further calculation

∠ACB=180

∘

−118

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By subtraction

∠ACB=62

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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

∘

By substituting the values

74

∘

+62

∘

+∠BAC=180

∘

On further calculation

∠BAC=180

∘

−74

∘

−62

∘

By subtraction

∠BAC=180

∘

−136

∘

∠BAC=44

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Therefore, the measure of each angle of the triangle is ∠A=44

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,∠B=74

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and ∠C=62

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.