Exterior angle theorem

The exterior angle of a triangle equals the sum of its two nonadjacent interior angles. It follows from the triangle angle-sum theorem and a linear pair.

Linear pair: A pair of adjacent angles whose noncommon sides form a straight line; their measures sum to 180 degrees. The exterior angle and its adjacent interior angle form this pair.
Triangle: A polygon with three sides and three interior angles. The theorem applies to a triangle and one side extended.
Triangle inequality theorem: A theorem stating that the sum of any two side lengths of a triangle exceeds the third. The exterior angle theorem helps establish that an exterior angle exceeds either remote interior angle, supporting side comparisons.
Exterior angle inequality theorem: A theorem in triangle geometry stating that an exterior angle exceeds either nonadjacent interior angle. It gives an inequality about each remote angle, unlike the theorem’s exact sum.
Euclidean geometry: The geometry of flat space based on Euclid’s postulates. The theorem follows from Euclidean triangle angle sums.
Exterior angle: An angle formed outside a polygon by one side and the extension of an adjacent side. It is the angle whose measure the theorem identifies.
Angle chasing: A method of solving geometry problems by combining known angle relationships. Replacing an exterior angle with the two remote angles creates equations in diagrams.
Triangle angle-sum theorem: The interior angles of every Euclidean triangle sum to 180 degrees. This is the underlying equality, while the exterior angle theorem isolates one angle.
Parallel postulate: Euclid’s postulate governing parallel lines, equivalent to the claim that triangle angles sum to 180 degrees. The standard proof relies on the Euclidean angle sum established using this postulate.
Interior angle: An angle inside a polygon, formed by two adjacent sides. The theorem compares the exterior angle with two interior angles.

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