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.
Therefore,
∠A + ∠B + ∠C
∠A + ∠A < ∠A + ∠B + ∠C
2∠A < 180o [Sum of all angles of a triangle]
∠A = 90o
Similarly,
∠B < 90o and ∠C < 90o
Hence, the triangle is acute angled.