**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

Example

**Worked**

Example

Example

**Key**

Examples

Examples

**Activities**

**Activity**

Answers

Answers

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

Example

o

o

o

Starter

Start on the left, work your way across doing the calculations in your head, and write down the answer.

START ANSWER

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

Start on the left, work your way across doing the calculations in your head, and write down the answer.

START ANSWER

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

….