A transversal cuts two lines such that a pair of alternate interior angles are 50° and 60°. Are the two lines parallel?

Class 9Lines and AnglesGeometry — Lines and Angles

ANo, because alternate interior angles are unequal (50° ≠ 60°).
BYes, because the angles are both acute.
CYes, because they sum to less than 180°.
DCannot be decided without more data.

Step-by-Step Solution

Lines are parallel only if a pair of alternate interior angles is EQUAL. Here 50° ≠ 60°, so the lines are not parallel.

Answer: A) No, because alternate interior angles are unequal (50° ≠ 60°).

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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