AQA · Mathematics · 8300

GCSE Maths: Angles: polygons

Geometry & Measures · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Angles: polygons (Corbettmaths Video 32), and every card links back to the exact page it came from. Practice tests are drawn from this deck’s own cards. Source material © Corbettmaths — used with attribution.

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  1. What is the formula for the sum of interior angles of an n-sided polygon?

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    (n - 2) × 180°

  2. How do you calculate each interior angle of a regular polygon with n sides?

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    Divide the sum of interior angles by n: [(n - 2) × 180°] ÷ n

  3. What is the sum of all exterior angles of any polygon?

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    360°, regardless of the number of sides.

  4. How do you calculate each exterior angle of a regular polygon with n sides?

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    360° ÷ n

  5. What is the relationship between an interior angle and its corresponding exterior angle in a polygon?

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    They are supplementary: interior angle + exterior angle = 180°

  6. If each exterior angle of a regular polygon is 20°, how many sides does it have?

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    18 sides. Use the formula: n = 360° ÷ exterior angle = 360° ÷ 20° = 18.

  7. Why do regular hexagons tessellate?

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    Each interior angle is 120°, and 360° ÷ 120° = 3, so three hexagons meet perfectly at each vertex with no gaps.

  8. Why do regular pentagons not tessellate?

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    Each interior angle is 108°, and 360° ÷ 108° = 3.33..., which is not a whole number, so pentagons cannot meet perfectly at vertices without gaps or overlaps.

  9. What is each interior angle of a regular octagon?

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    135°. Using [(8 - 2) × 180°] ÷ 8 = 1080° ÷ 8 = 135°.

  10. Why will a regular octagon not tessellate?

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    Each interior angle is 135°, and 360° ÷ 135° = 2.67..., which is not a whole number, so octagons cannot meet perfectly at vertices.

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