Lesson: Intermediate Problem Solving - 25t01

Practice: Using A Sketch

[Page 25 of 27]
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Answer each question that follows. Draw a diagram or sketch if you feel that it would help your answer to be more accurate or quicker. Click Continue after you've selected your answer.

1. Routes X, Y, and Z intersect to form a triangle. If route X and route Y intersect at a 20 degree angle and if Z is perpendicular to route X, at what angle do streets Z and Y intersect?
  50 degrees 60 degrees 70 degrees

This question is testing two basic geometric rules 1) the interior angles of a triangle equal 180 degrees and 2) perpendicular lines intersect at 90 degree angles (right angles). If upon reading this you realized immediately that since the three streets form a triangle and two of the angles are given (20 and 90 degrees), you could calculate the remaining angle without a sketch:

The internal angles of a triangle always add to 180, so the third angle must be 180 – 90 – 20 = 70 degrees.

Most questions are like this one in that some people will find a sketch useful while others won't bother. If you did draw a sketch you probably found that it took you a few seconds longer to do the problem, but those seconds are well worth it if the sketch helped you find the correct answer! This is especially true on early problems.

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