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Lines m and n are parallel and are cut by a transversal t. An angle at the m-intersection measures 116°. The angle alternate-exterior to it forms a linear pair with an angle . Find .

Class 7Lines and AnglesLines and Angles
  • A116°
  • B26°
  • C64°
  • D58°

Step-by-Step Solution

Two steps. First, alternate exterior angles between parallel lines are EQUAL, so that angle is also 116°. Second, forms a linear pair with it, so °. Trap: 116° is the answer to only the first step; 26° comes from subtracting from 90° instead of 180° (a linear pair is supplementary, not complementary).
Answer: C) 64°

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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