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Polygons (F)

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Polygons (F)

Explore polygons: name shapes, calculate interior and exterior angles, and use n-gon formulas to solve GCSE Foundation questions.

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Fascinating Fact:

In floor plans, a quadrilateral has interior angle sum = 360°, so angles 90, 110, and 80 force the last angle = 80, since 90 + 110 + 80 + 80 = 360.

In GCSE Maths, polygons include triangles, quadrilaterals and regular n-gons. You’ll use angle sum rules, exterior angles totalling 360°, and properties of regular polygons to find unknown angles accurately.

Key Terms

Polygon: A 2D shape made of straight line segments, such as triangles, quadrilaterals, and pentagons.
Interior angle sum: Total of the inside angles; for an n-gon it is (n − 2) × 180°.
Exterior angle (regular): Angle between a side and the extension of the next side; each equals 360° ÷ n in a regular polygon.

Frequently Asked Questions (Click to see answers)

How do I find the interior angle sum of a polygon?

Use (n − 2) × 180°, where n is the number of sides. For a pentagon, (5 − 2) × 180° = 540°.

What is the exterior angle of a regular polygon?

Each exterior angle in a regular n-gon is 360° ÷ n. For a regular nonagon, that’s 360° ÷ 9 = 40°.

How do I find a missing angle in a quadrilateral?

Add the known three angles and subtract from 360°. Example: 90° + 110° + 80° = 280°, so the missing angle is 360° − 280° = 80°.

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You can find more about this topic by visiting BBC Bitesize - Angles, lines and polygons

Author: Frank Evans (Specialist 11 Plus Teacher and Tutor)

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