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Question -

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



Answer -

In a ∆ABC,
Let ∠A < ∠B + ∠C
 
⇒∠A + ∠A < ∠A + ∠B + ∠C
⇒ 2∠A < 180°
⇒ ∠A < 90° (∵ Sum of angles of a triangle is 180°)
Similarly, we can prove that
∠B < 90° and ∠C < 90°
∴ Each angle of the triangle are acute angle.

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