**Introduction**

If one side of a triangle is extended, an **exterior angle** is formed. An exterior angle of a triangle forms a linear pair with the adjacent interior angle. The two non-adjacent interior angles to the exterior angle are called its **remote interior angles**. In the figure below, and are remote angles of .

In the second triangle above, we can see that the sum of the measures of the remote angles is equal to the measure of the exterior angle. That is, . Is this observation always true? In this post, we prove that it is indeed true

**Theorem**

The measure of the exterior angle of a triangle is equal to the sum of the measure sf its interior angles.

**Proof**

since the two angles are linear pair and therefore supplementary.

* by Addition Property of Equality

because the angle sum of a triangle is degrees.

by Addition Property of Equality**

From * and **, and both equal, ,

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This should be proven in neutral geometry. You cannot assume triangles have angle sum 180 in neutral geometry. That’s Euclidean geometry only.