Angles and Powers
The three diagrams below each show some of the sides from a regular polygon. In each case the
centre is marked by the letter O.
Shape 1 is part of a 12 sided polygon, Shape 2 is part of a 15 sided polygon and Shape 3 is part of an
18 sided polygon.
Your challenge is to calculate the sizes of all the angles in I have marked in red.
This is easier than it looks if you bear the following in mind.
1. Work out the exterior and interior angles of each shape.
2. Some of the lines from corners to the centre are drawn, some are not. If you add the
missing ones, then each diagram can be considered as looking like part of a pizza, where all
the pieces have sharp pints that meet in the centre (at O). Make sure you work out the size
of angle of each of these sharp points.
3. The lines from the centre to the corners are all the same length, therefore there are lots of
isosceles triangles.
You can either try to copy out these diagrams, or print them and cut them out!
Angles and Powers
In the following questions, you must remember three things.



3x2 does not mean three times x, and then square it. It means square x first, and then
multiply it by three.
x2 will always be positive.
50 – x2 means fifty take away a positive number, which means if x = -3, 50 – x2 = 41
Using the values a = -2, b = 3 and c = -4, calculate the values of the following:
1.
2.
3.
4.
5.
6.
a2 + c2
3abc
a(a – c)
2b2 + c
(2a)2
(3b)2
I have also emailed a paper, which I would like you to make a start on. You do not need to finish it.
As ever, try to highlight the things you are not 100% sure about, so that we can discuss them in class.