Question

if each angle of a triangle is less than the sum of the other two, show that the triangle is acute angled

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Answer 1

Answer:Let ∠A<∠B+∠C. Then,

2∠A<∠A+∠B+∠C⇒2∠A<180  

∘

⇒∠A<90  

∘

 

Similarly, we obtain ∠B<90  

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 and ∠C<90  

∘

 

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

Step-by-step explanation:

Answer 2

Answer:

let the sides of triangles be x ,y and z

given: each side of triangle >the sum of other two sides

now therefore,

x+y> z .........i

y+z>x ...........ii

x+z>y ..........iii

from EQ I, ii, and iii

we can conclude that if there's any angle which is 90° or more than 90° then one of three our equations must have equal or greater than sign(<)

therefore, all angles are less than 90°

→ triangle formed would be acute!

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