Question

If angle of triangle is less then the sum of the other two , show that the triangle is acute angled .

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Answer 1

Answer:

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:

Step-by-step explanation:

Let ∠A<∠B+∠C. Then,

2∠A<∠A+∠B+∠C⇒2∠A<180 degree

 ⇒∠A<90 degree

 Similarly, we obtain ∠B<90 degree   and ∠C<90 degree

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