Home MCQs GRE Quantitative Reasoning Question #8077
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GRE Quantitative Reasoning QUESTION #8077
Question 1

$\triangle RST$ is isosceles and $\angle RST = 40°$.

Compare:

Column A: The sum of the measures of the two angles of $\triangle RST$ that have equal measure

Column B: $120°$

  • Column A is greater
  • Column B is greater
  • The two quantities are equal
  • The relationship cannot be determined✔️
Correct Answer Explanation

In an isosceles triangle, two angles are equal. The sum of all angles in a triangle is $180°$.

Case 1: If $\angle RST = 40°$ is one of the two equal angles, then the two equal angles sum to $2 \times 40° = 80°$, and the third angle is $180° - 80° = 100°$.

Case 2: If $\angle RST = 40°$ is the unique angle (not one of the equal pair), then the two equal angles each measure $\frac{180° - 40°}{2} = 70°$, and their sum is $2 \times 70° = 140°$.

In Case 1, Column A = $80° < 120°$, so Column B is greater.

In Case 2, Column A = $140° > 120°$, so Column A is greater.

Since both cases are possible, the relationship cannot be determined.