Question

In each angle of the triangle is less than sum of other two ,show that triangle 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.

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Answer 2

Answer:

Hey!! Here is the answer...

Step-by-step explanation:

∠A+∠B+∠C. = 180                    .... (I)        ...............(angle sum property)

Let ∠A<∠B+∠C.

Then,

2∠A<∠A+∠B+∠C

⇒2∠A<180                                ,...........from (i)

⇒∠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.

Hope this helps........ : )