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# Angles and Polygons

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by

## Mr Mattock

on 16 January 2017

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#### Transcript of Angles and Polygons

Angles and Polygons
Explain why the centre angles are 72 .

How big are the red angles?

Why does this show that the exterior angles are also 72 .
L.O. - To find exterior and interior angles in regular polygons.
Find the size of an exterior and interior angle in this regular octagon.
Main Activity
Find the size of a single exterior and
interior angle in each picture.
e
e
e
e
e
e
The exterior angles of a polygon sum to 360
e = 360/n
where n = number of sides
Main Activity
Find the size of a single exterior and
interior angle in each picture.
60
120
90
90
72
108
60
120
51.42857...
128.5714...
45
135
40
140
36
144
Find the size of an exterior and interior angle in this regular octagon.
360/8
= 45
180 - 45
= 135
Worked
Example

Worked
Example

Key
Examples

Activities
Activity

Main Activity
Find the size of all the angles in this picture
Main Activity
o
o
Explain why the centre angles are 72 .
360/5 = 72 .
How big are the red angles?
54
Why does this show that the exterior angles are also 72 .
180 - 54 - 54 = 72
o
o
Exterior Angles
Not Exterior
Example
Calculate the values of x and y.
Example
Calculate the values of x and y.
x = 180 - 90
x = 90
y = 360 - 90 - 67
- 75 - 65
y = 63
o
o
Worked
Example

o
o
o
Starter

100 >> ÷ 5 , x 2 , + 5 , ÷ 9 , square , - 4 , x 2 , x 2 , ÷ 4 ………….

3 >> x 15 , - 5 , ÷ 8 , square , + 5 , ÷ 6 , x 12 , + 3 , ÷7 ………….

12 >> x 2 , ÷ 3 , x 8 , - 8 , ÷ 7 , x 4 , + 4 , ÷ 9 , x 12 ………….

54 >> ÷ 3 , - 8 , x 6 , x 2 , - 9 , ÷ 3 , - 10 , ÷ 9 , x 19 ………….

43 >> - 19 , ÷ 6 , square , ÷ 8 , + 16 , ÷ 9 , square , x 3 , x 2 ………….
Starter

100 >> ÷ 5 , x 2 , + 5 , ÷ 9 , square , - 4 , x 2 , x 2 , ÷ 4 …
21
….

3 >> x 15 , - 5 , ÷ 8 , square , + 5 , ÷ 6 , x 12 , + 3 , ÷7 …
9
….

12 >> x 2 , ÷ 3 , x 8 , - 8 , ÷ 7 , x 4 , + 4 , ÷ 9 , x 12 …
48
….

54 >> ÷ 3 , - 8 , x 6 , x 2 , - 9 , ÷ 3 , - 10 , ÷ 9 , x 19 …
57
….

43 >> - 19 , ÷ 6 , square , ÷ 8 , + 16 , ÷ 9 , square , x 3 , x 2 …
24
….
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