Angle facts let you calculate missing angles without measuring a diagram. First identify the shape or line relationship, then state the rule you are using. A straight line makes a half-turn, while angles around a point make a full turn. In parallel-line questions, corresponding angles and alternate angles are equal; co-interior angles total 180°. A bearing is a direction measured clockwise from north at the starting point and written with three digits. The return direction is opposite, so its bearing differs by 180°, adjusted to stay between 000° and 359°.
Learning objectives
- Use angle facts to calculate missing angles.
- Measure and interpret three-digit bearings.
Key ideas
Use straight-line, full-turn and triangle angle totals.
For parallel lines, corresponding and alternate angles are equal; co-interior angles are supplementary.
The interior angle sum depends on the number of polygon sides.
For a regular polygon, exterior angles are equal.
Measure bearings clockwise from north at the starting point. Write three digits.
Worked examples
Example 1
Find the return bearing for a journey with the given outward bearing.
The return direction differs by half a turn.
Answer
Example 2
Find each exterior angle of a regular octagon.
Answer
Question styles to prepare for
Original practice guidance aligned to the specification, not a count of past-paper appearances or a prediction. The AO labels below describe the intended practice focus, not official AQA mark allocations.
AO1 · Methods
Calculate an angle or measure and use a three-figure bearing.
AO2 · Reasoning
Give the geometric reason for each angle deduction.
AO3 · Problem solving
Connect bearings, parallel lines and angle facts to find a direction.
When a task asks you to explain, include a mathematical reason. When solving a problem, show how the information becomes a calculation, equation or diagram, then interpret your result.
Avoid this mistake
Bearings start at north at the starting point. For a return bearing, add or subtract half a turn as appropriate.
Try it yourself
Attempt each question before opening its answer.
Check 1: A triangle has angles 48° and 67°. Find its third angle.
Answer: 65°
Angles in a triangle total 180°, so 180 - 48 - 67 = 65.
Check 2: Find each exterior angle of a regular octagon.
Answer: 45°
One full turn is 360°. The eight equal exterior angles are each 360 ÷ 8 = 45°.
Explain it in your own words
- Explain the difference between corresponding and co-interior angles using your own diagram.
- Draw north lines and label a bearing of 120°.
- Derive the interior angle sum of a pentagon by splitting it into triangles.
Keep practising
Download the compact topic guide (PDF) · Practise this topic in Blitz · All foundation notes
Specification source
AQA Geometry specification · Assessment objectives. Checked 16 October 2026. Topic references identify related content; these notes do not cover every specification statement.