Question

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

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

Answer 1

True:
- m∠R > 90° — because R > S + T and R + S + T = 180°, so 2R > 180° ⇒ R > 90°.
- m∠S + m∠T < 90° — since S + T = 180° − R and R > 90°, 180° − R < 90°.
- m∠R > m∠T and m∠R > m∠S — from R > S + T and S + T ≥ T, S + T ≥ S, we get R > T and R > S.

False (not necessarily true):
- m∠S = m∠T
- m∠S > m∠T