Exterior Angle Theorem iof a Triangle

In this video, we are going to look at the exterior angle theorem of a triangle.

Exterior Angle Theorem: A measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles.

For example:
In the triangle, we are given two angle measures of $40\textdegree$ and $80\textdegree$ , and have to solve for the exterior angle “x”.

We could solve for the third angle in the triangle, which is $60\textdegree$ , and then subtract it from 180, since it lies on a straight line with the angle “x”. If we do this, we get that angle x = $120\textdegree$ .

This number may look familiar. We just used it to solve for the third angle in the triangle. This theorem works in all circumstances when trying to solve for the exterior angle.
$a+b=x$

This is known as the exterior angle theorem. The exterior angle will equal the sum of the other two nonadjacent interior angles.