Question

If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled

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Answer 1

Answer:

Let ∠A<∠B+∠C. Then,

2∠A<∠A+∠B+∠C⇒2∠A<180

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⇒∠A<90

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Similarly, we obtain ∠B<90

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and ∠C<90

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=> Each angle of the triangle is less than 90° and hence it is an acute-angled triangle.