Question

if each angle of triangle is less than the sum of the other two then prove that it is acute angle

Answer 1

Let ∠A ∠B and ∠C  be the interior angles of ΔABC 



Each angle is less than the sum of the other two angles (given) 



Consider ∠A < ∠B + ∠C 



=> ∠A < 180° - ∠A [∠A + ∠B + ∠C = 180°] 



=> 2 ∠A < 180° 



=> ∠A < 90° 



So ∠A is an acute angle  



ΔABC is an obtuse angled triangle.

@skb