Question

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

Answer 2

Answer:

let ABC be the triangle

Step-by-step explanation:

let angle A+B+C then 180 degree 2 a =180 ÷2 =90 it is acute angle