Question

If one angle of a triangle is greater than the sum of the other two, show
that the triangle is obtuse angled triangle
​

Answer 1

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 equation

So we get ∠B + ∠B > 180o – ∠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.

Need to Understand