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Two parallel lines are cut by a transversal. A pair of angles lies OUTSIDE the parallel lines and on OPPOSITE sides of the transversal. What is this pair called, and what is true of them?

Class 7Lines and AnglesLines and Angles
  • ACo-interior angles — they are supplementary.
  • BAlternate exterior angles — they are equal.
  • CAlternate interior angles — they are equal.
  • DCorresponding angles — they are supplementary.

Step-by-Step Solution

Outside the parallels plus opposite sides of the transversal names the ALTERNATE EXTERIOR pair, and such angles are equal. Trap: alternate interior angles are also equal but lie BETWEEN the parallels, so the position rules them out; and corresponding angles are equal, never supplementary.
Answer: B) Alternate exterior angles — they 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°).

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