geometry
posted by Laura on .
how can we prove that an exterior angle of a triangle has measure equal to the sum of the measures of the 2 interior angles remote from it

in triangle ABC extend BC to form the exterior angle at C, call that x
We know angle A + Angle B + angle C = 180
But angle C + x = 180, (by supplementary angle theorem)
so angle A + angle B + angle C = x + angle C
subtract angle C from both sides
angle A + angle B = x, the exterior angle
Therefore, the exterior angle of a triangle has measure equal to the sum of the measures of the 2 interior angles remote from it 
rocks 12