If each of a triangle is less than the sum of the other two, show that the triangle is acute angeld.
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Let ∠A<∠B+∠C. Then,
2∠A<∠A+∠B+∠C⇒2∠A<180
∘
⇒∠A<90
∘
Similarly, we obtain ∠B<90
∘
and ∠C<90
∘
=> Each angle of the triangle is less than 90° and hence it is an acute-angled triangle.
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