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A transversal cuts lines e and f. At the first crossing, the angle above the transversal on its right measures 68°; at the second crossing, the angle in exactly the same position measures 72°. Are e and f parallel?

Class 7Lines and AnglesLines and Angles
  • AYes — the two angles are close enough to count as equal.
  • BNo — corresponding angles would have to be EQUAL, and 68 is not 72.
  • CYes — 68 + 72 = 140°, which is less than 180°.
  • DNo — corresponding angles would have to add up to 180°.

Step-by-Step Solution

Same position at each crossing means these are CORRESPONDING angles, and they are equal only when the lines are parallel. Since 68 is not 72, e and f are not parallel. Trap: the last option borrows the co-interior rule (sum 180°) and pins it on corresponding angles; and "close enough" is never a geometry reason — a 4° gap means the lines slowly converge.
Answer: B) No — corresponding angles would have to be EQUAL, and 68 is not 72.

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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