Exterior Angle

Definition

An exterior angle is formed by one side of a polygon and the extension of an adjacent side. In polygons, each vertex has an exterior angle, which plays a key role in understanding the properties and relationships of angles, especially when dealing with triangles and their measures.

5 Must Know Facts For Your Next Test

1. For any polygon, the sum of all exterior angles is always 360 degrees, regardless of the number of sides.
2. An exterior angle is equal to the sum of the two opposite interior angles in a triangle, providing a way to find unknown angles.
3. When working with regular polygons, each exterior angle can be calculated by dividing 360 degrees by the number of sides.
4. The measure of an exterior angle increases as you decrease the number of sides in a polygon.
5. Exterior angles play a critical role in proofs and calculations involving triangles and other polygons, allowing for easier determination of unknown angle measures.

Review Questions

• How do exterior angles relate to the interior angles of a triangle?
  • Exterior angles in a triangle are directly related to its interior angles. Specifically, each exterior angle is equal to the sum of the two non-adjacent interior angles. This relationship helps in solving for unknown angle measures when working with triangles, emphasizing the importance of understanding both types of angles together.
• Explain why the sum of all exterior angles of any polygon equals 360 degrees, and provide an example to illustrate this concept.
  • The sum of all exterior angles in any polygon equals 360 degrees because each time you extend a side of the polygon, you create an angle that essentially represents a full rotation around that vertex. For example, in a pentagon with five sides, if you extend each side and measure each corresponding exterior angle, you will find that they add up to 360 degrees. This holds true regardless of how many sides the polygon has.
• Evaluate how knowledge of exterior angles can be applied in real-world scenarios or geometric proofs.
  • Understanding exterior angles is crucial in various applications such as architecture, engineering, and computer graphics. For example, when designing structures, knowing how to calculate exterior angles helps ensure that elements fit together correctly. In geometric proofs, recognizing that exterior angles can simplify calculations allows mathematicians to establish relationships between different shapes effectively, illustrating their importance beyond mere theoretical knowledge.

Related terms

Interior Angle: An interior angle is formed between two sides of a polygon and is located inside the polygon.

Supplementary Angles: Supplementary angles are two angles that add up to 180 degrees, which is important when considering relationships between interior and exterior angles.

Triangle Sum Theorem: The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees, which relates to the measurement of exterior angles.