Question

In triangle RST, m∠R > m∠S + m∠T. Which must be true of triangle RST? Check all that applym∠R > 90°

Answer 1

Answer:

In other words, A, B, D, E

Step-by-step explanation:

Answer 2

Answer: The correct statements are,

m∠R > 90°

m∠S + m∠T < 90°

m∠R > m∠T

m∠R > m∠S

Step-by-step explanation:

Here, RST is a triangle,

Therefore,  m∠R+m∠S+m∠T = 180° ⇒ m∠S+m∠T = 180° - m∠R

Given: m∠R > m∠S + m∠T

⇒ - m∠R < - (m∠S + m∠T) (by multiplying-1 on both sides)

⇒ 180°- m∠R < 180° - (m∠S + m∠T) (by adding 180° on both sides)

⇒ m∠S+m∠T < 180° - (m∠S + m∠T)

⇒ m∠S+m∠T+ m∠S+m∠T < 180° ( by adding m∠S + m∠T on both sides)

⇒ 2(m∠S+m∠T) < 180°

⇒ m∠S+m∠T < 90°

⇒ m∠R > 90° ( because m∠R+m∠S+m∠T = 180° )

Again, m∠R > m∠S + m∠T

⇒ m∠R > m∠S and  m∠R > m∠T

Thus, Option first second fourth and fifth are correct.

Note: m∠S = m∠T is only possible when m∠R=90° (but it is not given)

That is why m∠S = m∠T is not correct.

And, there are not enough information to prove m∠S > m∠T

That is why  m∠S > m∠T is also incorrect.