1. Interior Angles of Polygons
Learning objectives
16/01/2019
I can find the interior angles of a regular polygon
I can find missing angles in polygons

2. 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

3. Interior Angles of Polygons
Calculate the angle sum and interior angle of each of these regular polygons. 1 2 4 5 6 7 3
7 sides
10 sides
11 sides
12 sides
16 sides
20 sides
9 sides
to 1 dp
to 1 dp
Septagon/Heptagon
Nonagon
Decagon
Hendecagon
900o/128.6o
1260o/140o
1440o /144o
1620o /147.3o
Dodecagon
Hexadecagon
Icosagon
1800o /150o
2520o /157.5o
3240o /162o

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

5. Now try these ones yourself.
Interior Angles of Polygons y
120o
115o
85o
155o
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

6. Success Criteria I can find the interior angles of a regular polygon
I can find missing angles in polygons
10 ticks level 6 pack 5 page 27-28

7. Exterior Angles of Polygons
Learning objectives
16/01/2019
I can find the interior angles of a regular polygon
I can find missing angles in polygons

8. Exterior Angles of Polygons
Interior Angles
Exterior Angles
Use your protractor to measure the exterior angles of these shapes. Make a statement about your findings. ?
180o
Exterior angles of a polygon sum to 360o.

9. 72o 90o 108o 90o Square 4 Pentagon 5 3 60o 45o Hexagon 6 Octagon 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

10. 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

11. 1 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

12. 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

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

14. Success Criteria I can find the interior angles of a regular polygon
I can find missing angles in polygons
10 ticks level 6 pack 5 page 29

15. Static 6

17. Rose Demo
How many lines?
Sum (1 to 17)
(17 x 18)/2 = 153