- A68°
- B112°
- C22°
- D136°
Step-by-Step Solution
The road is a transversal of . The angle and lie between the lines on opposite sides of the road, so they are alternate interior angles: .
Answer: A) 68°
Two straight railway lines l and m are parallel (arrow marks). A straight road crosses both of them. Using the angle marked at line l, find the angle .
Class 9Lines and AnglesGeometry — Lines and Angles
Key idea: Parallel lines and a transversal — the eight angles
When a transversal cuts two lines, **8 angles** are created (4 at each intersection). They are grouped into four pairs:
**Corresponding angles** — same position relative to each intersection (e.g., upper-left and upper-left).
**Alternate interior angles** — between the two lines, on opposite sides of the transversal.
**Alternate exterior angles** — outside the two lines, on opposite sides of the transversal.
**Co-interior (allied) angles** — between the two lines, on the SAME side of the transversal.
**If the two lines are parallel**:
- Corresponding angles are EQUAL.
- Alternate interior angles are EQUAL.
- Alternate exterior angles are EQUAL.
- Co-interior angles are SUPPLEMENTARY (sum 180°).
**Corresponding angles** — same position relative to each intersection (e.g., upper-left and upper-left).
**Alternate interior angles** — between the two lines, on opposite sides of the transversal.
**Alternate exterior angles** — outside the two lines, on opposite sides of the transversal.
**Co-interior (allied) angles** — between the two lines, on the SAME side of the transversal.
**If the two lines are parallel**:
- Corresponding angles are EQUAL.
- Alternate interior angles are EQUAL.
- Alternate exterior angles are EQUAL.
- Co-interior angles are SUPPLEMENTARY (sum 180°).
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