Download basic angle theorems

GCSE Mathematics (1-9) 2015
How To Do it
G3Theory
Geometry -basic angle theorems - 3
apply the properties of angles at a point, angles at a point on a straight line,
vertically opposite angles; understand and use alternate and corresponding angles
on parallel lines; derive and use the sum of angles in a triangle (e.g. to deduce and
use the angle sum in any polygon, and to derive properties of regular polygons
1
Angles at a point
add up to 360.
w + x + y + z = 360
2
Angles on a straight line
add up to 180
w + x + y + z = 180
GCSE Mathematics (1-9) 2015
3
How To Do it
G3Theory
Vertically opposite angles
are equal.
w=y
x=z
w
(and w + x = 180 )
4
Alternate and corresponding angles
AB and CD are parallel
x and y are corresponding angles and are equal
x and z are alternate angles and are equal
( Or x=y, and y and z are vertically opposite so they
are equal )
x
z
y
GCSE Mathematics (1-9) 2015
5
How To Do it
Angles in a triangle
x + y + z = 360 (because these turn us through a
complete circle)
x=a-180 (angles on a straight line)
y=b-180
z=c-180
so
a-180 + b-180 + c-180 = 360
a+b+c -180 = 0
a+b+c = 180
Angles in a triangle add up to 180
6
Angle sum of a polygon
Suppose we have a polygon with n sides (shown for n =
7)
It contains n triangles
So the angles add up to 180n
This includes 360 at the middle point
So the interior angles add up to 180n - 360
7
Regular polygon
In a regular polygon, all angles are equal
so nx = 180n -360
so x = 180 - 360/n
For a hexagon ( 6 sided) for example,
x = 180 - 360/6 = 180 -60 = 120
G3Theory