Question

In triangle RST, mZR> m_S+ m2T. Which must be true of triangle RST? Check all that apply.

O mzR > 90°
OmZS + m2T < 90°
Om S = m_T
mZR>m_T
mZR > m_S
mzS>m_T

Answer 1

m∠R > 90°

m∠S + m∠T < 90°

m∠R > m∠T

m∠R > m∠S

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.