PSAT Math Multiple-Choice Question 75: Answer and Explanation

Question: 75

In the figure above, lines a and b are parallel. Which of the following pairs of angles must have equal degree measures?

I. 1 and 5

II. 2 and 7

III. 3 and 9

• A. I only
• B. II only
• C. III only
• D. II and III only

Correct Answer: D

Explanation:

D

The question asks for the pairs of angles that must have equal degree measures on a figure. Use the geometry basic approach. Start by labeling the figure with the given information. Mark lines a and b as parallel. In Statement (I), angles 1 and 5 do not have to be equal because a side of angle 1 is line c, which only intersects one parallel line in the figure; there is not enough information to determine whether any angle formed by line c is equal to one formed by line b. Thus, the angles in Statement (I) do not have to be equal; eliminate (A). Angles 2 and 7 are vertical angles (angles opposite each other when two lines intersect), and vertical angles must be equal. Therefore, the angles in Statement (II) have to be equal, so eliminate (C). Any time a line crosses two parallel lines, all of the small angles have the same measure and all of the big angles have the same measure. Angles 3 and 9 are both small angles formed where the same line (line d) crosses one of the parallel lines. Since the angles in Statement (III) must be equal, eliminate (B). Only Statements (II) and (III) are true. The correct answer is (D).