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

Answer:

Let ∠A<∠B+∠C. Then,

2∠A<∠A+∠B+∠C⇒2∠A<180∘

⇒∠A<90∘

Similarly, we obtain ∠B<90∘

and ∠C<90∘

=> Each angle of the triangle is less than 90° and hence it is an acute-angled triangle.