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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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