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Lines p and q are parallel and are cut by a transversal. One interior angle at p measures 71°. Find the angle that is vertically opposite to the co-interior partner of that 71° angle.

Class 7Lines and AnglesLines and Angles
  • A71°
  • B109°
  • C19°
  • D251°

Step-by-Step Solution

The co-interior partner is supplementary to 71°, so it measures 180 − 71 = 109°. Vertically opposite angles are equal, so the angle opposite it is also 109°. Trap: 71° is what you get by wrongly treating co-interior angles as equal — they are supplementary. 19° is the complement of 71°, which no rule here calls for.
Answer: B) 109°

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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