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Triangle Exterior Angle Theorem

Rule

Triangle Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.

Triangle with an exterior angle marked

Based on the diagram above, the following relation holds.

Proof

Consider a triangle and mark the exterior angle corresponding to

Triangle with an exterior angle marked

Notice that and form a linear pair. Therefore, their measures add up to Also, by the Triangle Angle Sum Theorem, the sum of the measures of the angles of add up Next, subtract the second equation from the first one. Finally, solve the last equation for to obtain the desired result.