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When two parallel lines are cut by a transversal, which pair of angles is SUPPLEMENTARY (sum 180°) rather than equal?

Class 9Lines and AnglesGeometry — Lines and Angles
  • ACo-interior (allied) angles
  • BCorresponding angles
  • CAlternate interior angles
  • DAlternate exterior angles

Step-by-Step Solution

For parallel lines, corresponding, alternate interior and alternate exterior angles are EQUAL, while co-interior (same-side interior) angles are supplementary, summing to 180°.
Answer: A) Co-interior (allied) angles

Key idea: Parallel lines and a transversal — the eight angles

When a transversal cuts two lines, **8 angles** are created (4 at each intersection). They are grouped into four pairs:

**Corresponding angles** — same position relative to each intersection (e.g., upper-left and upper-left).

**Alternate interior angles** — between the two lines, on opposite sides of the transversal.

**Alternate exterior angles** — outside the two lines, on opposite sides of the transversal.

**Co-interior (allied) angles** — between the two lines, on the SAME side of the transversal.

**If the two lines are parallel**:
- Corresponding angles are EQUAL.
- Alternate interior angles are EQUAL.
- Alternate exterior angles are EQUAL.
- Co-interior angles are SUPPLEMENTARY (sum 180°).

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