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Ignition Learning — Activity Sheet

Angles in parallel lines

Mathematics · Year 7

Name: ______________________Date: ____________

When a line called a transversal crosses two parallel lines, it creates several pairs of equal or related angles. Corresponding angles are in matching positions at each intersection and are equal. Alternate angles are on opposite sides of the transversal, between the parallel lines, and are also equal. Co-interior angles are on the same side of the transversal, between the parallel lines, and add up to 180°. Recognising these patterns lets you find unknown angles without measuring.

Example

If two parallel lines are crossed by a transversal and one angle is 70°, its corresponding angle (in the matching position at the other intersection) is also 70°. The co-interior angle next to it would be 180° − 70° = 110°.

Key terms

Transversal:: A line that crosses two or more other lines.
Corresponding angles:: Angles in matching positions where a transversal crosses two lines — equal when the lines are parallel.
Alternate angles:: Angles on opposite sides of a transversal, between two parallel lines — equal.
Co-interior angles:: Angles on the same side of a transversal, between two parallel lines — sum to 180°.

Questions

1. A transversal is:
- A parallel line
- A line that crosses two or more other lines
- A type of triangle
- A right angle
2. Corresponding angles are:
- Always different
- Equal when lines are parallel
- Always 90°
- Always add to 180°
3. Alternate angles are:
- On the same side
- On opposite sides of the transversal
- Always 180°
- Never equal
4. Co-interior angles:
- Are always equal
- Add up to 180° when lines are parallel
- Add up to 90°
- Are always 0°
5. Two parallel lines never:
- Cross a transversal
- Meet each other
- Have equal corresponding angles
- Exist together
6. If one angle formed by a transversal is 70°, its corresponding angle is:
- 20°
- 70°
- 110°
- 180°
7. Angles on a straight line add up to:
- 90°
- 180°
- 270°
- 360°
8. Two parallel lines are crossed by a transversal. One angle is 60°. What is its alternate angle?
- 30°
- 60°
- 120°
- 180°
9. Two parallel lines are crossed by a transversal. One angle is 65°. What is its co-interior angle?
- 65°
- 115°
- 125°
- 180°
10. If corresponding angles are NOT equal, the two lines are:
- Definitely parallel
- Definitely not parallel
- Always perpendicular
- Unrelated
11. Two parallel lines are crossed by a transversal. One angle is 105°. What is its corresponding angle?
- 75°
- 85°
- 105°
- 180°
12. Co-interior angles are found:
- On opposite sides of the transversal, between the parallel lines
- On the same side of the transversal, between the parallel lines
- Outside the parallel lines only
- On a single line only
13. If one co-interior angle is 130°, the other is:
- 50°
- 130°
- 230°
- 180°
14. Alternate angles are located:
- Between the parallel lines, on opposite sides of the transversal
- Outside the parallel lines
- On the same side only
- Never between the lines
15. A transversal crosses two parallel lines. One angle is 40°. What are the corresponding and alternate angles equal to?
- All are 40°
- Corresponding=40°, Alternate=40°, Co-interior=140°
- All are 140°
- All are different and unrelated
16. Two lines are crossed by a transversal, and a pair of alternate angles both measure 55°. What can you conclude?
- The lines must be parallel
- The lines cannot be parallel
- No conclusion can be drawn
- The lines are perpendicular
17. In a diagram, a pair of co-interior angles are found to be 100° and 90° (not adding to 180°). What does this tell you?
- The lines are definitely parallel
- The lines are not parallel
- There's no way to know
- All angles must be wrong
18. Two parallel lines are crossed by a transversal, creating an angle of 125°. What is the size of the alternate angle on the opposite side?
- 55°
- 125°
- 65°
- 180°
19. A transversal crosses two parallel lines. Which pair of angles are always equal — corresponding or co-interior?
- Co-interior
- Corresponding
- Neither
- Both are always equal
20. Understanding angles formed by parallel lines and a transversal is useful because it lets you:
- Guess angles randomly
- Calculate unknown angles logically using known angle relationships
- Avoid using a protractor entirely in all situations
- Only work with right angles

Answer key (parent copy)

1. A line that crosses two or more other lines
2. Equal when lines are parallel
3. On opposite sides of the transversal
4. Add up to 180° when lines are parallel
5. Meet each other
6. 70°
7. 180°
8. 60°
9. 115°
10. Definitely not parallel
11. 105°
12. On the same side of the transversal, between the parallel lines
13. 50°
14. Between the parallel lines, on opposite sides of the transversal
15. Corresponding=40°, Alternate=40°, Co-interior=140°
16. The lines must be parallel
17. The lines are not parallel
18. 125°
19. Corresponding
20. Calculate unknown angles logically using known angle relationships