1. Polygons
A polygon is a 2-D shape made when line segments enclose a region. A
The end points are called vertices. One of these is called a vertex. B
The line segments are called sides. E C D
These two dimensions are length and width. A polygon has no thickness.
2-D stands for two-dimensional.

2. Polygons A regular polygon has equal sides and equal angles.
In a convex polygon all of the interior angles are less than 180°.
All regular polygons are convex.
Define these key terms.
Define a regular polygon as having equal sides and equal angles.
Explain that in a concave polygon some of the interior angles are reflex angles.
In a concave polygon some of the interior angles are more than 180°.

3. Regular 3 4 5 6 7 8 9 10 11 12 16 20 Equilateral Triangle Square
Pentagon
Hexagon
Septagon/Heptagon
Octagon
Nonagon
Decagon
Hendecagon
Dodecagon
Hexadecagon
Icosagon

4. What’s happened? (mathematically speaking)
A hendecagon is laying eggsagons!
Thanks E.G (mathematical pie)

5. Interior Angles of Polygons
(n – 2) triangles
= (n – 2)180o
Find the connection between the number of sides and the number of triangles.
180o
180o
180o
180o
180o
4 sides
5 sides
6 sides
7 sides
Pentagon
Quadrilateral
3 x 180o = 540o 3
2 x 180o = 360o 2
The sum of the interior angles of an” n” sided polygon is?
180o
180o
180o
180o
180o
180o
180o
180o
180o
Hexagon
Heptagon/Septagon
4 x 180o = 720o 4
5 x 180o = 900o 5

6. Interior Angles of Polygons
Find the unknown angles below. x
100o
Diagrams not drawn accurately.
75o
95o w
115o
75o
110o
70o
3 x 180o = 540o
2 x 180o = 360o
540 – 395 = 145o
360 – 245 = 115o y
117o
121o
100o
125o
140o z
133o
137o
138o
105o
4 x 180o = 720o
5 x 180o = 900o
720 – 603 = 117o
900 – 776 = 124o

7. Interior Angles of Polygons
Now try these ones yourself. x
95o
88o 1 2
Diagrams not drawn accurately. z
125o
165o
150o
75o w 3 4
3 x 180o = 540o
540 – 418 = 122o
4 x 180o = 720o
720 – 595 = 125o
2 x 180o = 360o
360 – 240 = 120o
5 x 180o = 900o
900 – 780 = 120o

8. Exterior Angles of Polygons
Regular Polygons
72o
90o
120o
108o
90o
60o
Square 4
Pentagon 5
Equilateral Triangle 3
60o
45o
Hexagon 6
Octagon 8
Interior angles are 180 – 45 = 135o
Interior angles are 180 – 60 = 120o

9. Exterior Angles of Polygons
Calculate the exterior and interior angles of each of these regular polygons. 1 2 4 5 6 7 3
to 1 dp
7 sides
10 sides
11 sides
12 sides
16 sides
20 sides
9 sides
Septagon/Heptagon
Nonagon
Decagon
Hendecagon
51.4o/128.6o
40o/140o
36o/144o
32.7o/147.3o
Dodecagon
Hexadecagon
Icosagon
30o/150o
22.5o/157.5o
18o/162o

10. Exterior Angles of Polygons1 2 3 4
88o w
115o
108o x
80o
65o y
125o
Diagrams not accurately drawn
58o z
32o
55o
70o
45o
Calculate the value of the unknown angles.
Exterior Angles of Polygons
Angle w = 360 – ( ) = 145o
Angle x = 360 – ( ) = 49o
55o ? ?
122o
Angle y = 360 – ( ) = 70o
Angle z = 360 – ( ) = 36o

11. Exterior Angles of Polygons
Diagrams not accurately drawn
Now try these ones by yourself. 3 4
63o
73o y
115o
58o z
33o
55o
130o
45o 1 2
110o w
85o x
Angle w = 360 – ( ) = 140o
Angle x = 360 – ( ) = 55o
Angle y = 360 – ( ) = 69o
Angle z = 360 – ( ) = 119o

12. Find the number of sides
Challenge pupils to find the number of sides in a regular polygon given the size of one of its interior or exterior angles.
Establish that if we are given the size of the exterior angle we have to divide this number into 360° to find the number of sides. This is because the sum of the exterior angles in a polygon is always 360° and each exterior angle is equal.
Establish that if we are given the size of the interior angle we have to divide 360° by (180° – the size of the interior angle) to find the number of sides. This is because the interior angles in a regular polygon can be found by subtracting 360° divided by the number of sides from 180°.