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Lines r and s are parallel, and a transversal makes corresponding angles of ° and °. Find the measure of each of these two angles.

Class 7Lines and AnglesLines and Angles
  • A18°
  • B81°
  • C99°
  • D72°

Step-by-Step Solution

Corresponding angles between parallel lines are EQUAL, so → → . Each angle = °, and ° confirms it. Trap: 18° is the value of , not the angle; 99° is 180 − 81, which is what you get by wrongly setting the two corresponding angles supplementary instead of equal.
Answer: B) 81°

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°).

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