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

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.