exterior angles
In geometry, an exterior angle is formed when a side of a polygon is extended outward
In geometry, an exterior angle is formed when a side of a polygon is extended outward. This angle is formed by one side of the polygon and a line that is extended from the next side of the polygon. In other words, it is the angle that lies outside the polygon.
The measure of an exterior angle of a polygon is equal to the sum of the measures of its remote interior angles. The remote interior angles are the two angles that are inside the polygon and are not adjacent to the exterior angle.
For example, let’s consider a triangle. If we extend one of its sides, we can form an exterior angle at one of its vertices. To find the measure of this exterior angle, we need to determine the sum of the remote interior angles. Since a triangle has three interior angles, the sum of these angles is always 180 degrees. Therefore, the measure of the exterior angle is equal to 180 degrees minus the sum of the two remote interior angles.
Extending this concept to other polygons, the measure of an exterior angle of an n-sided polygon (regular or irregular) is given by the formula:
Measure of exterior angle = 360 degrees / n.
Understanding exterior angles is useful in various applications, such as calculating the measures of angles in polygons or determining properties of shapes in geometry.
More Answers:
Understanding Alternate Exterior Angles in Geometry | Congruence and ApplicationsExploring Corresponding Angles | The Relationship Between Parallel Lines and Transversals
Understanding Alternate Interior Angles | Definition, Properties, and Applications in Geometry