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

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 < 180 o [Sum of all angles of a triangle]

∠A = 90°

Similarly,

∠B < 90° and ∠C < 90°

Hence, the triangle is acute angled.