SAT Math Multiple Choice Question 540: Answer and Explanation

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Test Information

Question: 540

15. Main Street and 2nd Street run parallel to each other. Both are one-way streets. Main Street runs north, and 2nd Street runs south. The city is planning to build a new road, also one-way, that runs toward the southeast and cuts through both streets at an angle. Traffic turning off of Main Street would have to make a 125° turn onto the new road. What angle would traffic turning off of 2nd Street have to make turning onto the new road?

  • A. 55°
  • B. 65°
  • C. 125°
  • D. 235°

Correct Answer: A

Explanation:

A

Difficulty: Hard

Category: Additional Topics in Math / Geometry

Strategic Advice: This question does not provide a graphic, so sketch a quick diagram of the information presented. Be sure to show the direction of traffic for each street.

Getting to the Answer: The question describes two parallel streets, cut by a transversal. Start with that, and then add all the details.

Traffic traveling north on Main Street must make a 125° turn onto the new road. This is the angle between where the traffic was originally headed and where it is headed after it makes the turn. Traffic on 2nd Street is traveling south, the opposite direction. As shown in the diagram, the angle that the southbound traffic would make is supplementary to the corresponding angle made by the northbound traffic. When two parallel lines are cut by a transversal, corresponding angles are congruent, which means that cars turning off of 2nd Street will make a 180 – 125 = 55° turn onto the new road.

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