Question

147. If one angle of the triangle is greater than the
Sum of other two, show that the triangle is obtuse
angled.​

Answer 1

Answer:

Step-by-step explanation:

Consider ABC as a triangle

According to the question it can be written as

∠B>∠A+∠C....(1)

We know that the sum of all the angles in a triangle is 180  

∘

.

So we can write it as

∠A+∠B+∠C=180  

∘

 

So we get

∠A+∠C=180  

∘

−∠B

Substituting ∠A+∠C in equation (1) we get

∠B>180  

∘

−∠B

Add ∠B to both the sides of the equatio

So we get

∠B+∠B>180  

∘

−∠B+∠B

By addition we get

2∠B>180  

∘

 

By division we get

∠B>180/2

∠B>90  

∘

 

So we know that ∠B>90  

∘

 which means that ∠B is an obtuse angle

Therefore, it is proved that the triangle ABC is obtuse angled.

hope it helps