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

Respuesta :

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.

adioabiola

The statements which must be true of triangle RST are;

  • m∠R > 90°
  • m∠S + m∠T < 90°
  • m∠R > m∠T
  • m∠R > m∠S

Triangles and Angle measures

According to the stated premises;

  • m∠R > m∠S + m∠T

This in turn means that the angle measure of ∠R > angle measure of ∠S and ∠T.

Therefore, we can conclude that; m∠R > 90° and m∠S + m∠T < 90°

As such, certainly, m∠R > m∠T and m∠R > m∠S

Read more on angle measures of a triangle;

https://brainly.com/question/11664714

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