Sheet № 151 · Foundation + Higher · AQA · Edexcel · OCR
Alternate, Corresponding and Co-interior Angles –
Angles in parallel lines appear on every GCSE Maths exam paper. Whether it is AQA, Edexcel, or OCR, you will be asked to find missing angles using alternate, corresponding, and co-interior angle rules. This guide explains how to identify each type using the Z, F, and C/U shapes, works through Foundation and Higher examples, and highlights
§Key definitions
Question:
A transversal crosses two parallel lines. One of the alternate angles is 72°. Find the other.
Answer:
The missing angle is 72° (alternate angles are equal).
Q1 (Foundation):
A transversal crosses two parallel lines. A corresponding angle to an angle of 118° is marked. What is the corresponding angle?
Q2 (Foundation):
Two co-interior angles are x° and 135°. Find x.
Q3 (Higher):
A transversal crosses two parallel lines. One angle is (2x + 30)° and its alternate angle is (4x − 10)°. Find x and both angles.
§Formulas to memorise
Alternate angles are equal (Z-angles)
Corresponding angles are equal (F-angles)
Co-interior (allied) angles add up to 180° (C/U-angles)
Confirm the lines are parallel. — Look for arrows on the diagram. The rules only apply to parallel lines.
Identify the transversal — the line that crosses both parallel lines.
Decide the angle relationship. — Trace a Z, F, or C/U shape to determine whether the angles are alternate, corresponding, or co-interior.
Apply the rule. — Equal for alternate and corresponding; sum to 180° for co-interior.
State the reason. — Always write the name of the angle rule for full marks.
Worked example
A transversal crosses two parallel lines. One of the alternate angles is 72°. Find the other.
Working:
⚠ Common mistakes
- ✗Using parallel-line rules when lines are not parallel. If the diagram does not show arrows indicating parallel lines, you cannot apply these rules.
- ✗Confusing alternate and corresponding angles. Alternate angles are on opposite sides of the transversal (Z-shape); corresponding angles are on the same side (F-shape). Drawing the letter on the diagram helps.
- ✗Adding alternate or corresponding angles to 180°. Only co-interior angles sum to 180°. Alternate and corresponding angles are equal.
✦ Exam tips
- →Draw the Z, F, or C/U shape directly onto the exam diagram to help identify the correct rule.
- →If you cannot immediately see the relationship, extend the lines on the diagram to make the pattern clearer.
- →Many multi-step angle problems combine parallel-line rules with angles on a straight line or angles in a triangle. Be ready to use more than one rule.
- →Always name the rule in your written reason — "alternate angles" or "co-interior angles sum to 180°".