Angles & Polygons — GCSE Mathematics Revision
Revise Angles & Polygons for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to Constructions & LociWhat is Angles & Polygons?
Angles in a triangle sum to 180°. Angles in a quadrilateral sum to 360°. The sum of interior angles of any polygon with n sides is (n-2) × 180°. Each exterior angle of a regular polygon is 360° ÷ n. You also need angle facts: vertically opposite angles are equal, angles on a straight line sum to 180°, co-interior (allied) angles sum to 180°, and alternate angles are equal.
Step-by-step explanationWorked example
Find the interior angle of a regular hexagon. Sum of interior angles = (6-2) × 180° = 720°. Each angle = 720° ÷ 6 = 120°.
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Common mistakes
- 1Confusing alternate and co-interior angles — alternate angles are equal (Z-shape), co-interior angles sum to 180° (C/U-shape).
- 2Using the interior angle formula when the question asks for exterior angles, or vice versa.
- 3Forgetting that exterior angles of ANY polygon sum to 360°, not just regular ones.
- 4Not giving reasons for each step — examiners require you to name the angle fact used.
Angles & Polygons exam questions
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Angles & Polygons
Core concept
Angles in a triangle sum to 180°. Angles in a quadrilateral sum to 360°. The sum of interior angles of any polygon with n sides is (n-2) × 180°. Each exterior angle of a regular polygon is 360° ÷ n. Y…
Frequently asked questions
How do I find the number of sides from an interior angle?
Each exterior angle = 180° - interior angle. Number of sides = 360° ÷ exterior angle.
What angle facts do I need for parallel lines?
Alternate angles are equal (Z-angles), corresponding angles are equal (F-angles), and co-interior angles sum to 180° (C/U-angles).