4.1

Angles

Cambridge IGCSE Mathematics (0580)  · Unit 4: Geometry  · 10 flashcards

Angles is topic 4.1 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 4 — Geometry , alongside Angles in polygons, Parallel lines and Triangles.  In one line: An acute angle is an angle that measures greater than 0° and less than 90°.

This topic is examined across Paper 1 (Core) or Paper 2 (Extended) — non-calculator — and Paper 3 (Core) or Paper 4 (Extended) — calculator.

The deck below contains 10 flashcards — 6 definitions and 1 key concept — covering the precise wording mark schemes reward.  Use the 6 definition cards to lock down command-word answers (define, state), then move on to the concept and application cards to handle explain, describe and compare questions.

Key definition

An acute angle and provide an example

An acute angle is an angle that measures greater than 0° and less than 90°.

Example: an angle of 45° is an acute angle.

Questions this Angles deck will help you answer

Definition Flip

Define an acute angle and provide an example.

Answer Flip

An acute angle is an angle that measures greater than 0° and less than 90°.

Example: an angle of 45° is an acute angle.
Definition Flip

What is an obtuse angle? Give an example.

Answer Flip

An obtuse angle is an angle that measures greater than 90° and less than 180°. An example of an obtuse angle is 120°.

Definition Flip

What is a reflex angle? How does it differ from an obtuse angle?

Answer Flip

A reflex angle is an angle that measures greater than 180° and less than 360°. An obtuse angle is less than 180°, while a reflex angle is greater than 180°.

Key Concept Flip

Two angles form a straight line. One angle is 60°. What is the measure of the other angle?

Answer Flip

Angles on a straight line add up to 180°. Therefore, the other angle is 180° - 60° = 120°.

Definition Flip

Define 'complementary angles'. Give an example.

Answer Flip

Complementary angles are two angles that add up to 90°.

Example: 30° and 60° are complementary angles because 30° + 60° = 90°.
Definition Flip

What are 'supplementary angles'? Illustrate with an example.

Answer Flip

Supplementary angles are two angles that add up to 180°.

Example: 130° and 50° are supplementary angles because 130° + 50° = 180°.
Key Concept Flip

Three angles meet at a point. Their measures are 100°, 150°, and x. Find the value of x.

Answer Flip

Angles at a point add up to 360°. Therefore, 100° + 150° + x = 360°. Solving for x gives x = 360° - 250° = 110°.

Key Concept Flip

Explain the property of vertically opposite angles with a diagrammatic example.

Answer Flip

Vertically opposite angles are the angles opposite each other when two lines intersect. Vertically opposite angles are equal. For instance, if two lines cross, and one angle is 40°, the angle directly opposite is also 40°.

Definition Flip

What is a full turn in terms of degrees?

Answer Flip

A full turn is equal to 360 degrees. This represents a complete rotation around a point.

Key Concept Flip

If angle A and angle B are complementary, and angle A is 25 degrees, find the measure of angle B.

Answer Flip

Since complementary angles add up to 90 degrees, angle B = 90 - angle A = 90 - 25 = 65 degrees.

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3.3 Equations of lines 4.2 Angles in polygons

Key Questions: Angles

Define an acute angle and provide an example.

An acute angle is an angle that measures greater than 0° and less than 90°.

Example: an angle of 45° is an acute angle.
What is an obtuse angle? Give an example.

An obtuse angle is an angle that measures greater than 90° and less than 180°. An example of an obtuse angle is 120°.

What is a reflex angle? How does it differ from an obtuse angle?

A reflex angle is an angle that measures greater than 180° and less than 360°. An obtuse angle is less than 180°, while a reflex angle is greater than 180°.

Define 'complementary angles'. Give an example.

Complementary angles are two angles that add up to 90°.

Example: 30° and 60° are complementary angles because 30° + 60° = 90°.
What are 'supplementary angles'? Illustrate with an example.

Supplementary angles are two angles that add up to 180°.

Example: 130° and 50° are supplementary angles because 130° + 50° = 180°.

Tips to avoid common mistakes in Angles

More topics in Unit 4 — Geometry

Angles sits alongside these Mathematics decks in the same syllabus unit. Each uses the same spaced-repetition system, so progress in one informs the next.

Cambridge syllabus keywords to use in your answers

These are the official Cambridge 0580 terms tagged to this section. Mark schemes credit responses that use the exact term — weave them into your answers verbatim rather than paraphrasing.

angle degree acute obtuse right angle reflex straight line full turn vertically opposite angles on line angles at point complementary supplementary

Key terms covered in this Angles deck

Every term below is defined in the flashcards above. Use the list as a quick recall test before your exam — if you can't define one of these in your own words, flip back to that card.

An acute angle and provide an example
Obtuse angle? Give an example
Reflex angle? How does it differ from an obtuse angle
'complementary angles'. Give an example
'supplementary angles'? Illustrate with an example
Full turn in terms of degrees

Related Mathematics guides

Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.

How to study this Angles deck

Start in Study Mode, attempt each card before flipping, then rate Hard, Okay or Easy. Cards you rate Hard come back within a day; cards you rate Easy push out to weeks. Your progress is saved in your browser, so come back daily for 5–10 minute reviews until every card reads Mastered.