Angles – GCSE Maths

Foundation · Grade 2 · Non-calculator

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A handful of facts unlock almost every angle question at this grade. Angles on a straight line add to $180^{\circ }$. Angles around a point add to $360^{\circ }$. Angles in a triangle add to $180^{\circ }$; in a quadrilateral, $360^{\circ }$. Vertically opposite angles (the ones that make an X) are equal. An equilateral triangle has three $60^{\circ }$ angles; an isosceles triangle has two equal base angles.

The method is always: write the fact, write the sum, solve for the missing angle. Fourth angle of a quadrilateral with $85^{\circ }$, $110^{\circ }$ and $72^{\circ }$ is $360-267=93^{\circ }$. Reasons must be written in the accepted phrases — 'angles in a quadrilateral add to $360^{\circ }$' — because the reason is often a mark of its own.

Do not assume a triangle is isosceles or a line is straight unless the diagram is marked or the question says so. A picture that 'looks like' $90^{\circ }$ is not evidence.

Objectives

• A full turn is 360°. A straight line is 180°.
• Angles that meet at a point add to 360°.
• Two angles that make a straight line add to 180°.

Key points

• Find a missing angle on a straight line, around a point, in a triangle and in a quadrilateral.
• Use the properties of isosceles and equilateral triangles.
• Write the correct reason for each step in the standard wording.
• Chain two or more facts together to reach an angle that is not directly given.

Worked examples

Questions and answers

GCSE Maths angles questions and answers. Try each one, then open the answer. Easy questions come first.

Common mistakes

Most lost marks on this topic are one slip.

1. Using 360° for a straight line.

   A straight line is 180°.

2. Adding the triangle angles to 360°.

   A triangle sums to 180°.

3. Treating vertically opposite angles as angles that add to 180°.

   Opposite angles are equal. Adjacent ones add to 180°.

Exam tips

• Be ready to do this without a calculator. Paper 1 is the non-calculator paper.
• If the question says “show that”, the result is given. The marks are for the steps that reach it.
• The method is the same on AQA-style and Edexcel-style papers.
• If the question says 'give a reason', there is a mark for the words. Use the standard phrases exactly.
• Write each new angle on the diagram as you find it; it stops you losing track in a chain of steps.

Printable worksheet

The same questions are in a PDF you can print. Answers start on a later page.

Download worksheet (PDF)

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More on Angles

• Angles worked examples and method
  The method in order, key facts and the full lesson explanation
• Angles practice questions
  A second set of questions with answers, plus quick checks

AQA-style and Edexcel-style questions. Yumio is not affiliated with, endorsed by or connected to AQA, Pearson Edexcel or any other exam board.

Last updated 9 November 2026.