Question

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

Answer 1

$\huge\bigstar\underline\mathcal\blue{Answer:-}$

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.

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Answer 2

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 triangl