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A transversal cuts two lines c and d. A pair of alternate exterior angles measures 117° and 63°. Are c and d parallel?

Class 7Lines and AnglesLines and Angles
  • AYes — 117 + 63 = 180°, and alternate exterior angles are supplementary.
  • BYes — one angle is obtuse and the other acute, as parallel lines require.
  • CNo — alternate exterior angles would have to be EQUAL, and 117 is not 63.
  • DNo — the two angles would have to add up to 90°.

Step-by-Step Solution

Alternate exterior angles are equal when the lines are parallel. Here 117° and 63° are unequal, so c and d are not parallel. Trap: the first option borrows the CO-INTERIOR rule (sum 180°) and applies it to alternate exterior angles — the sum being 180° is exactly what tempts students here, but it proves nothing for this pair.
Answer: C) No — alternate exterior angles would have to be EQUAL, and 117 is not 63.

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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