Question

if each angle of a traingle is less than the sum of the other two then show that the traingle is acute angled​

Answer 1

Answer:

Let ∠A, ∠B and ∠C be the interior angles of ΔABC.

It is given that each angle is greater than the sum of the other two angles.

Consider ∠A > ∠B + ∠C

⇒ ∠A > 180° – ∠A  [∠A + ∠B + ∠C = 180°]

⇒ 2∠A > 180°

⇒ ∠A > 90°

Thus, ∠A is an obtuse angle.

Similarly, we will get ∠B is an obtuse angle and ∠C is an obtuse angle.

This means all the angles of ΔABC are obtuse, which is not possible.

So, the given condition should be: " One angle is greater than the sum of the other two angles".

Hence, ΔABC is an obtuse angled triangle.