Q. 14

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

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.


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