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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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:
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.