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The exterior angle theorem states that the measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles. An explanation of the concept, an example, and exercises for practice.
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The Exterior Angle Theorem
An exterior angle of a triangle is an angle outside the triangle that forms a linear pair with one of the angles of the triangle. The opposite interior angles ( remote interior angles ) of an exterior angle are the two nonadjacent interior angles of a triangle. The measure of an exterior angle of a triangle is equal to the sum of the measures of the two opposite interior angles.
Example: x is an exterior angle at T. 1 and 2 are the opposite interior angles of x. Therefore, m x = m 1 + m 2.