Question

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

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 isosceles triangle