Three lines a, b and c are cut by the transversal t. Using the marked angles, which two lines are parallel?

Class 7Lines and AnglesLines and Angles

Ab and c
Ba and c
CAll three lines
Da and b

Step-by-Step Solution

Between a and b, the co-interior angles on the right of t are

10 6^{\circ}

and

7 4^{\circ}

;

106 + 74 = 180

, so a ∥ b. Below b the angle on the right of t is

18 0^{\circ} - 7 4^{\circ} = 10 6^{\circ}

, and with

8 2^{\circ}

at c this gives

18 8^{\circ} \neq = 18 0^{\circ}

, so c is not parallel to b (or to a).

Answer: D) a and b

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.

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