Understanding Exterior Angles | Definition, Theorems, and Properties

Exterior angle of a polygon

In geometry, an exterior angle of a polygon is an angle formed outside the polygon by extending one of its sides

In geometry, an exterior angle of a polygon is an angle formed outside the polygon by extending one of its sides. Each polygon has multiple exterior angles, one for each side of the polygon. To identify the exterior angle of a polygon, you need to select a side and extend it to form an angle with the adjacent side. The exterior angle will always be adjacent and supplementary to the interior angle of the polygon at that vertex.

The exterior angle can be measured in degrees and is equal to the sum of the two interior angles that are adjacent to it. This relationship is known as the Exterior Angle Theorem, which states that the measure of the exterior angle of a polygon is equal to the sum of the measures of its remote interior angles.

For example, consider a triangle. If you extend one side of the triangle, you will create an exterior angle. This angle is formed by the extended side and the adjacent side of the triangle. According to the Exterior Angle Theorem, it is equal to the sum of the two remote interior angles of the triangle.

The concept of exterior angles becomes even more evident in polygons with more than three sides. For each side, you can extend it to create an exterior angle. The sum of all the exterior angles of any polygon, regardless of the number of sides, is always 360 degrees. This property is known as the Exterior Angle Sum Theorem.

In summary, the exterior angle of a polygon is an angle formed outside the polygon by extending one of its sides. It is equal to the sum of the two remote interior angles, and the sum of all exterior angles in any polygon is always 360 degrees.

More Answers: