Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryHard
A surveyor is measuring angles of a complex intersection. One angle of a transversal intersecting two parallel lines is measured as 4x + 10 degrees. Its corresponding angle is measured as 6x - 20 degrees. What is the value of x?
- A10
- B25
- C20
- D15
Show answer & explanationAnswer & explanation
Correct answer: D. 15
When a transversal intersects two parallel lines, corresponding angles are equal. Therefore, we can set the two expressions equal to each other: 4x + 10 = 6x - 20. Subtract 4x from both sides: 10 = 2x - 20. Add 20 to both sides: 30 = 2x. Divide by 2: x = 15.
Why the other options are wrong
- A. Incorrect. This would be the result if 4x + 10 = 6x - 10, or similar error.
- B. Incorrect. This might be from incorrect algebra, e.g., 2x = 50.
- C. Incorrect. This would be the result if 4x + 10 + 6x - 20 = 180 (consecutive interior angles), but these are corresponding angles.
Corresponding Angles (Parallel Lines)
When a transversal intersects two parallel lines, corresponding angles are located in the same relative position at each intersection and are always congruent (equal in measure).
- Form an 'F' shape visually.
- One angle is interior, the other is exterior.
- They are on the same side of the transversal.
- Their measures are equal.
Memory trick: Parallel lines are 'Partners', Transversal 'Travels' through them.