3. Angle A in triangle ABC is obtuse. Can angle B or angle C be obtuse? Explain your reasoning

Question

Mathematics

Kennedy Montes

16 November, 21:18

3. Angle A in triangle ABC is obtuse. Can angle B or angle C be obtuse? Explain your reasoning

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Answers (2)

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Lena Hurley · Answer 1

No, angle B or angle C can't be obtuse.

Step-by-step explanation:

It is given that:

Angle A in triangle ABC is obtuse.

This means that:

∠A > 90°

Now, let us assume that:

Angle B is obtuse.

i. e. ∠B > 90°

Hence, we get that the sum of two angle is greater than 180 degree. (i. e. ∠A+∠B > 180°)

hence, the sum of all the three angles will be greater than 180 degrees.

But we know that in order to form a triangle the sum of all the three angles must be equal to 180 degree.

Arjun Austin · Answer 2

No. To be obtuse the angle has to be over 90 degrees. All triangles should add up to 180 degrees. If angle A is at the smallest degree it can be (90) then that leaves 90 degrees to be split between angle B and C. Therefore they would have to both be less than 90 degrees making them both acute angles.