Exterior Angles Theorem
What is an exterior angle?
An exterior angle is the angle made between the outside of one side of a shape and a line that extends from the next side of the shape.
Interior and Exterior Angles Examples
Explore Exterior Angles
In the applet below, manipulate the vertices of the triangle. What do you notice remains constant? *Note: In geogebra and in later math classes, angles are generally represented by letters of the Greek alphabet.[size=150] [math]a[/math], [math]\beta[/math], [math]\gamma[/math], [math]\delta[/math], [math]\epsilon[/math],[/size] and [math]\zeta[/math] are all Greek letters.
Answer the following questions.
What do you notice about each exterior angle and the interior angle it is connected to (the adjacent interior angle)? What do they form?
What do you notice about the measure of the interior angles not connected (the non-adjacent interior angles) to an exterior angle?
The Exterior Angle Theorem
Based on your observations, the Exterior Angle Theorem would be as follows: (fill in the blanks)[br][br]The measure of an exterior angle of a triangle is _______________________ of the measures _____________________.