- A180
- B99
- C81
- D90
Step-by-Step Solution
Co-interior (same-side interior) angles are supplementary, summing to 180°. If they are equal, each = 180 ÷ 2 = 90°.
Answer: D) 90
Two parallel lines are cut by a transversal so that the two interior angles on the same side of the transversal are equal. What is the measure of each (in degrees)?
Class 7Lines and AnglesLines and Angles
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.
- **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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