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:

Step-by-step explanation:

Let a, b and c be three angles of a triangle. Then, a+b+c =180° ……….(1)

If a+b <c, then using equation (1), we get;

c+c < 180° => 2c <180° => c <180°/2

=> c < 90°

Similarly, we get; a<90° and b<90°

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

Answer 2

Answer:

Hey mate!! 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........ : )