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# Regular Polygons

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by

## Mr Mattock

on 21 November 2017

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#### Transcript of Regular Polygons

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

Worked
Example

Key
Examples

Activities
Activity

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
Full transcript