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A transversal cuts two lines l and m. The two interior angles on the same side of the transversal measure 104° and 74°. Are l and m parallel?

Class 7Lines and AnglesLines and Angles
  • AYes — co-interior angles are always supplementary, whatever the lines.
  • BNo — if l and m were parallel these would add to 180°, but 104 + 74 = 178°.
  • CYes — one angle is obtuse and the other acute, which is what parallel lines need.
  • DNo — if l and m were parallel these two angles would have to be equal.

Step-by-Step Solution

Co-interior (same-side interior) angles are supplementary ONLY when the two lines are parallel. Here 104 + 74 = 178°, which is not 180°, so l and m are not parallel. Trap: the last option treats co-interior angles as EQUAL — they are supplementary, not equal. The first option assumes the very thing being tested.
Answer: B) No — if l and m were parallel these would add to 180°, but 104 + 74 = 178°.

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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