if each angle of a triangle is less than the sum of the other two, sow that the triangle is acute angled.
Let ∠A, ∠B and ∠C be the interior angles of ΔABC.
It is given that each angle is less 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 acute angle.
Infact, all the angles are acute.
Hence, ΔABC is an obtuse angled triangle.