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.
