Grade four, Edexcel GCSE Maths

Revision Notes

What is a polygon?

A polygon is a flat (plane) shape with n straight sides.

eg A triangle is a polygon with 3 sides

eg A quadrilateral polygon with 4 sides

eg 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

eg A regular polygon with 3 sides is an equilateral triangle

eg A regular polygon with 4 sides is a square 

Working with angles in polygons
  1. TOTAL OF INTERIOR ANGLES = 180° × (n – 2)
    (because the polygon can be split into n -2 triangles)
  2. TOTAL OF EXTERIOR ANGLES = 360°
    (this exterior angles rule is the same for ANY number of sides!)

eg For a hexagon (n=6):

Angles in a Hexagon, IGCSE & GCSE Maths revision notes

a + b + c + d + e + f = 180° × (6 – 2) = 720°

p + q + r + s + t + u = 360°

For REGULAR Polygons:

For REGULAR Polygons:

3. EXTERIOR ANGLE = 360 ÷ n

4. INTERIOR ANGLE = 180 – Exterior Angle

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

Example

The diagram shows an irregular pentagon.
Work out the value of x.

Polygon-Example-REWRITTEN-5-3-20, IGCSE & GCSE Maths revision notes

This is an irregular pentagon (5 sides) so:

1. Total Interior Angles=180(5-2)=540°

Putting in the information from the diagram gives:

(3x + 5) + x + (x + 40) + 95 + (2x – 20)  =  540

Simplifying:

   7x + 120  =  540

And solving:

    7=  420

  =  60

Question

Edexcel GCSE Maths Notes

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