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

Answer 1

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

Answer 2

rocks 12

Answer 3

Very brilliant answer like the way of explanation,
Thanks to help

Answer 4

Jiskha