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Assertion (A): When a transversal cuts two parallel lines, each pair of co-interior angles is supplementary. Reason (R): Co-interior angles always sum to 90°. Which is correct?

Class 7Lines and AnglesLines and Angles
  • AA is true but R is false.
  • BBoth A and R are true.
  • CA is false but R is true.
  • DBoth A and R are false.

Step-by-Step Solution

Co-interior angles between parallel lines are supplementary (sum to 180°), so A is true. R says they sum to 90°, which is false.
Answer: A) A is true but R is false.

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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