Question

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

Answer 1

In a $\Delta ABC$, let $\angle A<\angle B+\angle C$

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

$\Rightarrow 2\angle A<{180}^{\circ }$ $(\because$ sum of angles of a triangle is ${180}^{\circ })$

$\Rightarrow \angle A<{90}^{\circ }$

Similarly, we can prove that

$\angle B<{90}^{\circ }$ and $\angle C<{90}^{\circ }$

$\therefore$ Each angle of the triangle is an acute angle.