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

Let a triangle ABC having angles.

It is given that the sum of two angles are less than third one.

We know that the sum of all angles of a triangle equal to 180°.

Similarly we can prove that

Since, all angles are less than 90°.
Hence, triangle is acute angled.