If each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled.

Proof

Let ABC be a triangle,

Now,

< +___________________ (i)

< +___________________ (ii)

< +___________________ (iii)

2 < ++ [From equation (i)]

2 < 180° [Sum of angles of triangle]

< 90° ________________ (a)

Similarly,

< 90°__________________ (b)

< 90°__________________ (c)

From equation (a), (b) and (c), each angle is less than 90°

Therefore triangle is an acute angled Proved.