ACT (Enhanced)MathematicsMedium
A surveyor is measuring angles for a new construction project. If two parallel lines are intersected by a transversal, and one of the interior angles on the same side of the transversal measures 115 degrees, what is the measure of the other interior angle on the same side?
- A115 degrees
- B75 degrees
- C25 degrees
- D65 degrees
Show answer & explanationAnswer & explanation
Correct answer: D. 65 degrees
When two parallel lines are intersected by a transversal, interior angles on the same side are supplementary, meaning they add up to 180 degrees. If one angle is 115 degrees, the other is 180 - 115 = 65 degrees.
Why the other options are wrong
- A. This would be the measure if they were alternate interior angles or corresponding angles, which they are not.
- B. Incorrect subtraction, possibly from 100 or 150.
- C. Incorrect subtraction or misunderstanding of supplementary angles.
Angles with Parallel Lines
When a transversal intersects two parallel lines, specific relationships exist between the angles formed, such as corresponding, alternate interior, alternate exterior, and consecutive interior (same-side interior) angles.
- Corresponding angles are equal.
- Alternate interior angles are equal.
- Alternate exterior angles are equal.
- Consecutive interior angles are supplementary (sum to 180°).
Memory trick: Parallel lines are like railroad tracks, angles have special relationships.