Corresponding
Same relative position. They are equal.
Learning Objectives
- identify corresponding angles;
- identify alternate angles;
- identify co-interior angles;
- calculate missing angles on parallel lines;
- recognise when parallel-line rules may be used.
Introduction
A transversal is a line that crosses two or more other lines.
When the crossed lines are parallel, the angles repeat in a predictable pattern. Understanding the positions comes before choosing a rule.
Key Notes
Alternate
Inside the parallel lines on opposite sides of the transversal. They are equal.
Co-interior / Allied
Inside the parallel lines on the same side. They add to 180°.
Applying the Relationships
One angle formed by a transversal is 68°.
Its corresponding angle is 68°.
Its alternate angle is 68°.
The co-interior angle is 180°−68°=112°.
Recognition Guide
- Corresponding angles often form an F shape.
- Alternate angles often form a Z shape.
- Co-interior angles often form a C or U shape.
These rules require parallel lines. Look for arrow markings or a statement that the lines are parallel.
Try It: Parallel-Line Angle Families
🧠 Let’s Think Together
Two parallel lines are crossed by a transversal. One acute angle is 68°. Equal-angle relationships copy 68° to the matching corresponding and alternate positions. Every neighbouring obtuse angle is 180° − 68° = 112°.
The diagram therefore contains only two angle sizes: 68° and 112°.
Worked Examples
Example 1: Corresponding angles
A corresponding angle to 74° is 74° because corresponding angles between parallel lines are equal.
Example 2: Co-interior angles
If one co-interior angle is 63°, its partner is 180° − 63° = 117°.
Example 3: Algebra
Corresponding angles are (3x + 10)° and (5x − 30)°. They are equal, so 3x + 10 = 5x − 30 and x = 20.
Practice Questions
Foundation- If a corresponding angle is 73°, find its matching angle.
- If an alternate angle is 118°, find the other alternate angle.
- A co-interior angle is 64°. Find its partner.
- Corresponding angles are (3x+10)° and (5x−30)°. Find x.
- Co-interior angles are (2x+20)° and (4x−8)°. Find x.
- An acute angle made by a transversal is 38°. List all eight angles formed at the two intersections.
✅ Check Your Work
Show practice answers
- 73°.
- 118°.
- 116°.
- 3x+10=5x−30, so x=20.
- 6x+12=180, so x=28.
- Four angles are 38° and four are 142°.
Common Mistakes
- Using parallel-line rules when the lines are not marked or stated to be parallel.
- Confusing alternate angles with co-interior angles.
- Saying co-interior angles are equal instead of checking that they total 180°.
Exam Focus
Name the relationship used in every step. Look first for parallel-line arrow markings, then identify the angle positions before calculating.
Summary
- Corresponding angles are equal.
- Alternate angles are equal.
- Co-interior angles total 180°.
- Use these rules only when the lines are parallel.