Geometry & MeasuresTopic Summary

Knowledge Organiser: Angle Facts

Part of Angle Facts · GCSE GCSE Mathematics revision

This topic summary covers Knowledge Organiser: Angle Facts within Angle Facts for GCSE Mathematics. Revise Angle Facts in Geometry & Measures for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 5 of 5 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 5 of 5

Practice

14 questions

Recall

12 flashcards

Knowledge Organiser: Angle Facts

Key Terms
  • Acute angle: An angle less than 90°
  • Right angle: Exactly 90°
  • Obtuse angle: Between 90° and 180°
  • Reflex angle: Between 180° and 360°
  • Vertically opposite: Equal angles formed by two intersecting lines
  • Supplementary: Two angles that add up to 180°
Must-Know Facts
  • Angles on a straight line add up to 180°
  • Angles around a point add up to 360°
  • Vertically opposite angles are EQUAL
  • A right angle is exactly 90°
  • Always give a reason (e.g. "angles on a straight line") in your answer
  • Angles in a triangle sum to 180°; in a quadrilateral to 360°
Key Methods
  • Identify which angle fact applies, then write an equation
  • Straight line: a + b = 180 → solve for unknown
  • Around a point: a + b + c + ... = 360 → solve for unknown
  • Vertically opposite: set the two expressions equal and solve
Key Formulas
  • Angles on a straight line: sum = 180°
  • Angles around a point: sum = 360°
  • Vertically opposite angles: equal
  • Right angle = 90°; straight angle = 180°; full turn = 360°
Common Mistakes
  • Angles on a straight line vs around a point: Check whether angles share a straight line (sum 180°) or surround a point (sum 360°)
  • Vertically opposite ≠ supplementary: Vertically opposite angles are EQUAL, not adding to 180°
  • Not giving a reason: Exam questions require you to state the angle rule used — "angles on a straight line" etc.
  • Assuming angles look equal: Never assume angles are equal from appearance — you must use a rule to justify

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Keep building this topic

Read this section alongside the surrounding pages in Angle Facts. That gives you the full topic sequence instead of a single isolated revision point.

Practice Questions for Angle Facts

An angle measures 135°. What type of angle is this?

  • A. Acute
  • B. Obtuse
  • C. Right angle
  • D. Reflex
1 markfoundation

Two angles on a straight line are 73° and 107°. A student says: 'These two angles must be equal because they are on a straight line.' Is the student correct? Give a reason for your answer.

2 markshigher

Quick Recall Flashcards

What is an acute angle?
An angle that is greater than 0° and less than 90°. Examples: 30°, 45°, 89°
What is a reflex angle?
An angle that is greater than 180° and less than 360°. Examples: 200°, 270°, 359°

14 questions on Angle Facts — practise free

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