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

Let's analyze the given inequality and determine which statements must be true for triangle RST.

Given: m∠R > m∠S + m∠T

m∠R > 90°: We cannot determine whether this statement is true based on the given inequality. The sum of angles in a triangle is always 180°, so ∠S + ∠T = 180° - ∠R. However, we don't have enough information to determine if ∠R is greater than 90°.

m∠S + m∠T < 90°: This statement is true because if m∠S + m∠T is less than 90°, it means that the sum of the other two angles (m∠R) must be greater than 90° to satisfy the inequality m∠R > m∠S + m∠T.

m∠S = m∠T: We cannot determine whether this statement is true based on the given inequality. The inequality only provides a relationship between m∠R, m∠S, and m∠T, but it doesn't give us information about the equality of m∠S and m∠T.

m∠R > m∠T: This statement is true based on the given inequality m∠R > m∠S + m∠T. Since m∠T is part of the sum m∠S + m∠T, if m∠R is greater than the sum, it must be greater than m∠T as well.

m∠R > m∠S: This statement is true based on the given inequality m∠R > m∠S + m∠T. Since m∠S is part of the sum m∠S + m∠T, if m∠R is greater than the sum, it must be greater than m∠S as well.

m∠S > m∠T: We cannot determine whether this statement is true based on the given inequality. The inequality only provides a relationship between m∠R, m∠S, and m∠T, but it doesn't give us information about the relationship between m∠S and m∠T.

So, the statements that must be true for triangle RST are:

m∠S + m∠T < 90°

m∠R > m∠T

m∠R > m∠S