**Regular Polygons**

Starter

A dodecagon is the proper name for a 12-sided shape.

How many degrees would be in a dodecagon in total?

All the angles in the dodecagon are the same size. How big would each angle be?

Why are the exterior angles (marked e) the same as the centre angles (marked c)?

**L.O. - To find interior and exterior 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

How big

is the sum of

the angles marked c?

What does this say about the sum of the exterior angles?

c

c

c

c

c

c

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

Why are the exterior angles (marked e) the same as the centre angles (marked c)?

e

How big

is the sum of

the angles marked c?

360 degrees

What does this say about the sum of the exterior angles?

Also

360

c

c

c

c

c

c

o

Find the size of an exterior and interior angle in this regular octagon.

360/8

= 45

180 - 45

= 135

Starter

A dodecagon is the proper name for a 12-sided shape.

How many triangles would a dodecagon break down

into?

12

How many degrees would be in a dodecagon in total?

12 x 180 - 360 = 1800 degrees

How would your answers change if I changed dodecagon for chiliagon (1000 sides)?

1000 x 180 - 360 = 179640 degrees

**Worked**

Example

Example

**Worked**

Example

Example

**Key**

Examples

Examples

**Activities**

**Activity**

Answers

Answers

150

o

The diagram shows two sides of a regular

polygon, separated by an angle of 150 degrees.

Work out the number of sides of the polygon.

150

o

The diagram shows two sides of a regular

polygon, separated by an angle of 150 degrees.

Work out the number of sides of the polygon.

Exterior angle = 30 degrees.

360/30 = 12 sides.

Main Activity

Find the size of all the angles in this picture

Main Activity