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Two angles lie BETWEEN two parallel lines and on the SAME side of the transversal that cuts them. Which statement about this pair is correct?

Class 7Lines and AnglesLines and Angles
  • AThey are equal.
  • BThey are complementary.
  • CThey are vertically opposite, so they are equal.
  • DThey are supplementary.

Step-by-Step Solution

Between the parallels and on the same side of the transversal describes CO-INTERIOR (allied) angles, and these sum to 180°. Trap: the first option is the single most common error in this chapter — co-interior angles are supplementary, not equal. Vertically opposite angles share a vertex, which this pair does not.
Answer: D) They are supplementary.

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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