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

Given:

Each angle of a triangle is less than the sum of the other two.

To do:

 We have to show that the triangle is acute angled.

Solution:

Let in a $\triangle ABC$, $\angle A < \angle B + \angle C$

This implies,

$\angle A + \angle A < \angle A + \angle B + \angle C$

$2\angle A < 180^o$

$\angle A < 90^o$

Similarly,

$\angle B < 90^o$

$\angle C < 90^o$

Hence, each angle of the triangle is an acute angle.

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Updated on: 10-Oct-2022

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