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Lines u and v are parallel, and a transversal meets u at a right angle. What angle does the transversal make with v, and why?

Class 7Lines and AnglesLines and Angles
  • A90°, because corresponding angles between parallel lines are equal.
  • B90°, because co-interior angles between parallel lines are equal.
  • CIt can be any measure — the right angle applies only at u.
  • D180°, because the two angles form a linear pair.

Step-by-Step Solution

The angle at v corresponds to the 90° angle at u, and corresponding angles between parallel lines are equal, so it is also 90°. A transversal perpendicular to one of two parallel lines is perpendicular to the other as well. Trap: the second option gets the right number by the WRONG rule — co-interior angles are supplementary, not equal (they happen to be 90 + 90 = 180 here, which hides the error).
Answer: A) 90°, because corresponding angles between parallel lines are equal.

Key idea: Parallel lines and a transversal

When a transversal crosses two **parallel** lines, eight angles form (four at each intersection). They come in special pairs:

- **Corresponding angles**: same position at each intersection (e.g. both top-left). **Equal**.
- **Alternate interior angles**: between the parallel lines, on opposite sides of the transversal. **Equal**.
- **Alternate exterior angles**: outside the parallel lines, on opposite sides of the transversal. **Equal**.
- **Co-interior (same-side interior) angles**: between the parallel lines, on the same side of the transversal. **Supplementary** (sum to 180°).

These are the rules you'll use most. Sketch the figure and label what you know — the rest follows quickly.

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