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Triangle Exterior Angle Theorem

See also: Triangle exterior angle definition

Theorem:   An exterior angle of a triangle is equal to the sum of the opposite interior angles.

In the figure above, drag the orange dots on any vertex to reshape the triangle. The exterior angle at B is always equal to the opposite interior angles at A and C.

Although only one exterior angle is illustrated above, this theorem is true for any of the three exterior angles.

A related theorem

Because an exterior angle is equal to the sum of the opposite interior angles, it follows that it must be larger than either one of them. Stated more formally:

Theorem: An exterior angle of a triangle is always larger then either opposite interior angle.

Drag the vertices of the triangle around to convince yourself this is so.

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Other triangle topics

General

Perimeter / Area

Triangle types

Triangle centers

Congruence and Similarity

Solving triangles

Triangle quizzes and exercises