Question

one angle of triangle is greater than the sum of the other two wind can you say about the measure of this angle? what type of triangle is this.​

Answer 1

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.