1. ©G Dear2008 – Not to be sold/Free to use
Mathematic
(Preliminary)
Geometry
Angles in a Triangle
Stage 6 - Year 11
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©G Dear2008 – Not to be sold/Free to use

2. Angle Sum of a Triangle ao bo co ao + bo + co = 180o Proof: xo
xo = bo (Alternate angles
between parallel lines) yo ao bo co
yo = co (Alternate angles
between parallel lines)
ao + xo + yo = 180 o (Straight angle)
Therefore ao + bo + co = 180 o

3. Angle Sum of a Triangle ao bo co ao + bo + co = 180o Angle Sum mo
m = 70
60o

4. Angle Sum of a Triangle ao bo co ao + bo + co = 180o Angle Sum
a + 2a + 3a = 180
6a = 180
÷ ÷6
3ao
a = 30
2ao

5. Exterior Angle of a Triangleao bo co
ao + bo = co
Proof:
xo = ao (Alternate angles
between parallel lines) ao bo co
yo = bo (Corresponding angles
between parallel lines) xo yo
xo + yo = co (adjacent angles)
Therefore ao + bo = co

6. Exterior Angle of a Triangleao bo co
ao + bo = co
m =
Exterior angle
of a triangle.
m = 110 mo
50o
60o

7. Exterior Angle of a Triangleao bo co
ao + bo = co
Exterior angle
of a triangle.
m + 50 = 80
80o
m = 30 mo
50o

8. Exterior Angle of a Triangleao bo co
ao + bo = co
Exterior angle
of a triangle.
2m + 2m = 80
80o
4m = 80
÷ ÷4
m = 20
2mo
2mo