Geometry and TrigonometryMediumAngle relationships with a transversal
Geometry and Trigonometry practice question
Two parallel roads are crossed by a straight path. At the first road, the acute angle between the path and the road measures 3x + 15 degrees. At the second road, the obtuse angle between the path and the road, on the same side of the path, measures 5x + 5 degrees. What is the value of x?
- A. 20Correct
- B. 5
- C. 30
- D. 10
Answer: A. 20
An acute and an obtuse angle on the same side of a transversal between parallel lines are supplementary: (3x + 15) + (5x + 5) = 180, so 8x = 160 and x = 20. (The angles are 75° and 105°.)
Why the other answers are wrong
- B. 5
- 5 comes from setting the two expressions equal (3x + 15 = 5x + 5); an acute and an obtuse angle can't be equal.
- C. 30
- 30 comes from 8x + 20 = 260 or a similar arithmetic slip.
- D. 10
- 10 comes from 8x = 80, halving 160.
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