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

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

Angle Sum of a Triangle ao bo co ao + bo + co = 180o Angle Sum -110 -110 mo m = 70 60o

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

Exterior Angle of a Triangle ao 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

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

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

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