PSAT Math Multiple-Choice Question 697: Answer and Explanation

Question: 697

In the below drawing, lines AB and CD are parallel, and line EF is a transversal. How many angles made from the given lines measure 60 degrees?

• A. 1
• B. 2
• C. 4
• D. 6

Correct Answer: C

Explanation:

(C) The angle next to the 120-degree angle on line AB is 60 degrees because two angles on a given line (supplementary angles) must add up to 180 degrees.

The angle directly opposite that first 60 degree angle must also be 60 degrees, because angles opposite one another (called vertical angles) are equal. Furthermore, that vertical angle is along line EF with the 120-degree angle. So the sum of these supplementary angles must also be 180 degrees, making the vertical angle 60 degrees.

Because lines AB and CD are parallel and line EF is a transversal, opposite interior angles are also congruent. Therefore, the acute angle along line CD is also 60 degrees.

Because that angle is 60 degrees, the acute angle across from it (also along line CD) is also 60 degrees since angles opposite one another (vertical angles) must be congruent.