1. Polygons A polygon is a shape made from only straight edges
Polygons are named on the basis of how many sides they have
You need to learn the following names:
Some of the names get silly…
Sides
Polygon Name 12
Dodecagon
5 sides
4 sides 13
Triskaidecagon
3 sides 14
Tetrakaidecagon
Triangle
Quadrilateral
Pentagon 19
Enneadecagon 20
Icosagon
100000
Megagon
8 sides
10100
Googolgon
6 sides
7 sides
Hexagon
Heptagon
Octagon

2. Regular and irregular polygons
A regular polygon is one with all sides the same and angles the same
To describe all other regular polygons, just put the word ‘regular’ in front of their name
Because you often use regular triangles and quadrilaterals, they have special names:
Equilateral Triangle
Regular pentagon
Regular hexagon
Square
An irregular polygon has sides and angles that vary
Irregular heptagon
Irregular octagon

3. Regular and irregular polygons
1. Label each shape with its name :
Regular heptagon
Irregular pentagon
Irregular hexagon
Regular octagon
2. Explain why the following shapes are not regular polygons:
a) Rhombus
b) Isosceles triangle
c) Rectangle
______________________________________
Sides are equal but angles aren’t
______________________________________
Only 2 sides and angles equal
______________________________________
Angles are equal but sides aren’t

4. Angles in Polygons
The angles inside the shape at each corner are called interior angles
The angle between pairs of adjacent sides are called exterior angles
Can you spot the connection between interior and exterior angles?
They add up to 180o at any corner
Interior angle
Exterior angle +
In this section, we also look at rules for:
the sum of the exterior angles of any polygon
the sum of the interior angles of any polygon
the exterior angle of a regular polygon
the interior angle of a regular polygon

5. Sum of exterior angles
What is the sum of the exterior angles of a polygon?
For a polygon with n sides:
the exterior angles sum to 360o

6. Proving that the sum of the interior angles of a triangle sum to 180o
In year 7 you saw the following proof:
Alternate angles
Alternate angles
Therefore

7. Sum of interior angles
The interior angles of polygons can be split into triangles…
Triangle
Quadrilateral
Pentagon
Hexagon
1 triangle
2 triangles
3 triangles
4 triangles
Sides
Triangles
Sum of interior angles
Can you spot the connection between the number of sides and the sum of the interior angles?
Sum of interior angles
number of sides
If a polygon has n sides…

8. Interior and exterior angles for regular polygons
For any polygon with n sides:
Eg regular octagon
Exterior angles sum to 360o
Interior angles sum to
For a regular polygon:
Exterior angle
Interior angle
Eg regular octagon
Exterior angle
Interior angle

9. Regular and irregular polygons
1. Label each shape with its name :
2. Explain why the following shapes are not regular polygons:
a) Rhombus
b) Isosceles triangle
c) Rectangle
______________________________________
______________________________________
______________________________________

10. The sum of exterior and interior angles for any polygon
1. Work out the sum of the interior angles of an octagon
2. Work out the sum of the exterior angles of a heptagon
3. Work out the sum of the interior angles of a 12-sided polygon
4. Find the missing angles b) a)

11. Angles in regular polygons
For any polygon with n sides:
For a regular polygon:
Interior angle
Exterior angle +
Exterior angle
The exterior angles sum to 360o
Interior angle
The interior angles sum to
1. Use the rules to complete the following table:
Polygon
Sides
Sum of exterior angles
Sum of interior angles
For regular shape
Exterior angle
Interior angle
Pentagon
Hexagon
Nonagon
Decagon
Pendedecagon

12. 2. Dave says “There is a regular polygon with exterior angles of 50o”
2. Dave says “There is a regular polygon with exterior angles of 50o”. Explain why Dave is wrong
3. John says “There is a regular polygon with interior angles of 170o”. Explain why John is correct
4. A pupil has three tiles. One is a regular octagon, one is a regular hexagon, and one is a square. The side length of each tile is the same.
The pupil says the hexagon will fit exactly like this.
Show calculations to prove that the pupil is wrong.

13. Problem solving with polygons
1. Find the number of sides of a regular polygon with:
a) exterior angles of 15o
b) interior angles of 135o
c) an interior angle sum of 2700o
2. Use the rules in reverse to complete the following table:
Name
Sides
Sum of interior angles
For regular shape
Exterior angle
Interior angle 30
162
1080

14. 3. The diagram shows a regular octagon.
Find the size of angle x
4. Find the size of the smallest angle is this irregular pentagon