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

Question

Philoid · Accepted Answer

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.