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