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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Practice Questions for Angle Facts
An angle measures 135°. What type of angle is this?
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.
Quick Recall Flashcards
14 questions on Angle Facts — practise free
Instant marking, adaptive difficulty, and 12 spaced repetition flashcards. Free until your GCSEs.
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