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GRE Quantitative Practice, Standard Multiple-Choice

Question 4

In a certain parallelogram, the size of one interior angle exceeds that of another interior angle by D degrees. Which of the following expressions represents the degree measure of the smaller angle?

  1. 90 – D
  2. 180 – equation system
  3. 120 – D
  4. 90 – equation system
  5. 180 – D

Explanatory Answer

Let x equal the degree measure of the smaller angle, and let (x + D) equal the degree measure of the larger angle. The two angles are by definition supplementary, which means that their degree measures total 180:

x + (x + D) = 180

Solving for x yields the expression in choice (D), which is the correct answer.