Table of Contents
Introduction to Exterior Angle Theorem
An exterior angle theorem states that the sum of the exterior angles of a triangle is equal to the sum of the interior angles. In other words, the exterior angles are supplementary. This theorem is useful for determining the size of a triangle, as well as its interior and exterior angles.
What is an Exterior Angle?
An exterior angle is an angle that is created outside of a polygon. This angle is found by extending the sides of the polygon until they intersect.
Exterior Angle Property
The exterior angle of a polygon is the angle between two adjacent sides.
Exterior Angle Property of a Triangle
The exterior angle of a triangle is the angle between the triangle’s exterior side and the extension of its opposite side.
Properties of Exterior Angle
The exterior angle of a polygon is the angle between two adjacent sides, outside the polygon.
The exterior angle is always less than or equal to the sum of the interior angles.
The exterior angle is always 180 degrees minus the sum of the interior angles.
Exterior Angle Theorem
The exterior angle theorem states that the measure of the exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Exterior Angle Theorem Proof
A triangle has 180 degrees in total. The exterior angle theorem states that the sum of the exterior angles of a triangle is 180 degrees. This theorem is proven by constructing a proof diagram.
In the diagram, triangle ABC has exterior angles A, B, and C. Angle A is the sum of angles B and C. Angle B is the sum of angles A and C. Angle C is the sum of angles A and B. Since angles A, B, and C are all equal, the exterior angle theorem is proven.
