A transversal cuts lines a and b. A pair of alternate interior angles both measure 58°. What can you conclude?

Class 7Lines and AnglesLines and Angles

Aa is parallel to b.
Ba is perpendicular to b.
Ca and b meet at an angle of 58°.
DNothing can be decided — equal angles never prove anything.

Step-by-Step Solution

If a transversal makes a pair of alternate interior angles equal, the two lines must be parallel — this is the converse of the alternate-interior-angle property. Since 58° = 58°, a is parallel to b. Perpendicular would need a 90° angle, so that option is a guess at the wrong property.

Answer: A) a is parallel to b.

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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