Knowledge Organiser: Angles in Polygons
This topic summary covers Knowledge Organiser: Angles in Polygons within Angles in Polygons for GCSE Mathematics. Revise Angles in Polygons in Geometry & Measures for GCSE Mathematics with 12 exam-style questions and 3 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 10 of 10 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 10 of 10
Practice
12 questions
Recall
3 flashcards
Knowledge Organiser: Angles in Polygons
Key Terms
- Interior angle: Angle inside a polygon at each vertex
- Exterior angle: Angle formed outside the polygon at each vertex
- Regular polygon: All sides and angles are equal
- Transversal: A line crossing two other lines
- Polygon: A closed 2D shape with straight sides
Must-Know Facts
- Interior angle sum = (n − 2) × 180°
- Exterior angle sum = ALWAYS 360° for any polygon
- Interior + exterior angle at same vertex = 180°
- Each interior angle of a regular polygon = (n − 2) × 180° ÷ n
- Each exterior angle of a regular polygon = 360° ÷ n
- Hexagon interior sum = 720°; each regular angle = 120°
- To find number of sides: n = 360° ÷ exterior angle
Key Formulas
- Interior sum = (n − 2) × 180°
- Each interior (regular) = (n − 2) × 180° ÷ n
- Each exterior (regular) = 360° ÷ n
- Interior + exterior = 180°
Common Mistakes
- Wrong formula for interior sum: Use (n − 2) × 180°, not n × 180°
- Confusing interior and exterior: Exterior angles always sum to 360°; interior sum depends on n
- Regular vs irregular: "Each interior angle" formula only works for regular polygons where all angles are equal
- Finding n from an angle: Set 360° ÷ n = exterior angle, then solve for n
- Not subtracting known angles: In an irregular polygon, subtract the known angles from the interior sum
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Practice Questions for Angles in Polygons
What is the sum of the interior angles of a hexagon?
Explain how the formula (n − 2) × 180° for the sum of interior angles of a polygon is derived.
Quick Recall Flashcards
12 questions on Angles in Polygons — practise free
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