How to answer "Give reasons" questions in GCSE Maths

What it means

When a question asks you to give a reason, you must name the specific mathematical rule that justifies your statement. Vague language ("because of geometry", "from the diagram") scores zero. Use the exact terminology from the curriculum.

What examiners want

• For parallel lines: "alternate angles are equal", "corresponding angles are equal", "co-interior angles sum to 180°"
• For straight lines and points: "angles on a straight line sum to 180°", "angles at a point sum to 360°"
• For triangles: "angles in a triangle sum to 180°", "base angles of an isosceles triangle are equal"
• For circles: name the specific theorem ("angle at the centre is twice the angle at the circumference", "angle in a semicircle is 90°", "alternate segment theorem", etc.)

Worked example

AB is parallel to CD. Find angle x and give your reason.

x = 65°. Reason: alternate angles are equal (AB is parallel to CD).

Common mistakes

• Writing "because they are the same" or "from the diagram"
• Mixing up alternate and corresponding angles
• Saying "Z-angle" or "F-angle" — examiners want the formal term ("alternate" / "corresponding")
• Forgetting to mention that the lines are parallel when using parallel-line reasons

Marks tip

Each angle reason is usually worth 1 mark on top of the angle value. Write a separate line per reason — do not jam them all together.