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Lines p and q are parallel (arrow marks) and are cut by a transversal. The two marked angles are ° and °. Find the value of .

Class 9Lines and AnglesGeometry — Lines and Angles
  • A15
  • B37
  • C35
  • D17

Step-by-Step Solution

Both marked angles lie between the parallel lines on the same side of the transversal, so they are co-interior: . (Check: )
Answer: C) 35

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°).

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