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Angles in Polygons (Cambridge O Level Maths)

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Angles in Polygons

What is a polygon?

  • A polygon is a flat (plane) shape with n straight sides
    • For example:
      • A triangle is a polygon with 3 sides
      • A quadrilateral polygon with 4 sides
      • A pentagon is a polygon with 5 sides
  • In a regular polygon all the sides are the same length and all the angles are the same
    • A regular polygon with 3 sides is an equilateral triangle
    • A regular polygon with 4 sides is a square

What are the sums of angles in polygons?

  • To be able to work with angles in polygons, you need to be able to find the sums of angles in polygons
  • To find the sum of the interior angles in a polygon of n sides, use the rule
    • SUM OF INTERIOR ANGLES = 180° × (n – 2)
      • because the polygon can be split into n -2 triangles
    • For regular polygons, this can then be divided by n to find each individual angle
  • The sum of the exterior angles in any polygon always add up to 360°
    • TOTAL OF EXTERIOR ANGLES = 360°
      • The exterior angles are the angles extended out from each side on a straight line
      • It is important to note that the interior and exterior angles for each side lie on a straight line so they add up to 180° 

Angles in a Hexagon, downloadable IGCSE & GCSE Maths revision notes

Interior & Exterior Angle for Regular Polygon, IGCSE & GCSE Maths revision notes

Examiner Tip

  • Make sure you identify whether you are dealing with a regular or irregular polygon before you start a question

Worked example

The exterior angle of a regular polygon is 45°.

Write down the name of the polygon.

The formula for the exterior angle of a regular polygon is Exterior space Angle equals fraction numerator 360 degree over denominator n end fraction. 

Substitute the 45 for the exterior angle.

45 degree equals fraction numerator 360 degree over denominator n end fraction

Solve by rearranging.

table attributes columnalign right center left columnspacing 0px end attributes row n equals cell 360 over 45 end cell row blank equals 8 end table

Write down the name of a shape with 8 sides.

Octagon

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    Amber

    Author: Amber

    Expertise: Maths

    Amber gained a first class degree in Mathematics & Meteorology from the University of Reading before training to become a teacher. She is passionate about teaching, having spent 8 years teaching GCSE and A Level Mathematics both in the UK and internationally. Amber loves creating bright and informative resources to help students reach their potential.