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A transversal cuts parallel lines g and h. A pair of alternate interior angles measures ° and °. Find .

Class 7Lines and AnglesLines and Angles
  • A35
  • B33
  • C70
  • D7

Step-by-Step Solution

Alternate interior angles between parallel lines are EQUAL, so → . Both angles then measure 95°. Trap: 33 comes from wrongly making them supplementary: → → . Only CO-INTERIOR angles are supplementary; alternate interior angles are equal.
Answer: A) 35

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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