# geometry

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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

• geometry -

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

• geometry -

rocks 12

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