Question

In triangle RST, if mZR is greater than m2S + m2T, which must be true of triangle RST? Check all that apply:

a. mZR > 90°
b. m2S + m2T < 90°
c. mZS = mZT
d. mZR > mXT
e. mZR > mZS
f. m2S > mZT

Answer 1

In triangle RST where the measure of angle R is greater than the measure of angle S plus twice the measure of angle T, it must be true that angle R is greater than 90 degrees and the sum of the measure of angle S and twice the measure of angle T is less than 90 degrees. Additionally, angle R must be greater than the measure of angle S alone, but there is not enough information to assess the other properties.

Step-by-step explanation:

In triangle RST, if the measure of angle R (m∠R) is greater than the measure of angle S plus twice the measure of angle T (m∠S + 2m∠T), we can determine certain properties about the triangle:

• a. m∠R > 90°: This is true because the sum of angles in a triangle is 180°, and if m∠R is greater than the sum of the other two angles, it must be greater than half of 180°, which is 90°.
• b. m∠S + 2m∠T < 90°: If m∠R > m∠S + 2m∠T and m∠R > 90°, then m∠S + 2m∠T must be less than 90° by the background concept of angles in a triangle.
• c. m∠S = m∠T: There isn't enough information given to determine if this is true.
• d. m∠R > m∠T: This is not necessarily true as we do not know the relationship between m∠T and the other angles individually.
• e. m∠R > m∠S: This must be true as m∠R is greater than the combination of m∠S and twice m∠T, so it must be greater than m∠S alone.
• f. m∠S > m∠T: This is not provable with the given information, we cannot determine the individual relationship between m∠S and m∠T.