Angles in polygons
Cambridge IGCSE Mathematics (0580) · Unit 4: Geometry · 9 flashcards
Angles in polygons is topic 4.2 in the Cambridge IGCSE Mathematics (0580) syllabus , positioned in Unit 4 — Geometry , alongside Angles, Parallel lines and Triangles. In one line: A regular polygon has all sides and all angles equal.
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 9 flashcards — 2 definitions and 3 key concepts — covering the precise wording mark schemes reward. Use the 2 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.
A regular polygon and give an example
A regular polygon has all sides and all angles equal.
Questions this Angles in polygons deck will help you answer
- › What is the sum of the exterior angles of *any* polygon?
- › Explain the relationship between interior and exterior angles at a vertex of a polygon.
- › What formula gives the sum of the interior angles of an n-sided polygon?
What is the sum of the interior angles of a hexagon?
The sum of interior angles of an n-sided polygon is (n-2) * 180°. For a hexagon (n=6), the sum is (6-2) * 180° = 720°.
Define a regular polygon and give an example.
A regular polygon has all sides and all angles equal.
Calculate the size of each interior angle in a regular pentagon.
The sum of interior angles in a pentagon is (5-2) * 180° = 540°. Each interior angle in a *regular* pentagon is 540° / 5 = 108°.
What is the sum of the exterior angles of *any* polygon?
The sum of the exterior angles of *any* polygon (regular or irregular) is always 360 degrees. Each exterior angle is formed by extending one side of the polygon.
If an interior angle of a regular polygon is 150°, how many sides does the polygon have?
Each exterior angle is 180° - 150° = 30°. Since the sum of exterior angles is 360°, the polygon has 360° / 30° = 12 sides.
Explain the relationship between interior and exterior angles at a vertex of a polygon.
At each vertex, the interior angle and the exterior angle are supplementary, meaning they add up to 180°. The exterior angle is formed by extending one side.
Define an irregular polygon and give an example.
An irregular polygon is a polygon where the sides and angles are not all equal. A rectangle is an irregular polygon if its sides are not equal in length (i.e., it is not a square).
A quadrilateral has angles 70°, 80°, and 120°. What is the size of the fourth angle?
The sum of angles in a quadrilateral is 360°. Therefore, the fourth angle is 360° - (70° + 80° + 120°) = 360° - 270° = 90°.
What formula gives the sum of the interior angles of an n-sided polygon?
The formula to calculate the sum of the interior angles of a polygon with n sides is (n-2) * 180 degrees.
Key Questions: Angles in polygons
Define a regular polygon and give an example.
A regular polygon has all sides and all angles equal.
Define an irregular polygon and give an example.
An irregular polygon is a polygon where the sides and angles are not all equal. A rectangle is an irregular polygon if its sides are not equal in length (i.e., it is not a square).
Tips to avoid common mistakes in Angles in polygons
- ● Lock these two formulas into your brain: the sum of the interior angles is (n-2)*180 degrees; each interior angle in a regular polygon is [(n-2)*180]/n.
- ● When finding trig solutions, consider the unit circle and ensure your graph covers all possible values you might need.
More topics in Unit 4 — Geometry
Angles in polygons 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.
Key terms covered in this Angles in polygons 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.
Related Mathematics guides
Long-read articles that go beyond the deck — cover the whole subject's common mistakes, high-yield content and revision pacing.
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