Exterior angle

Definition

An exterior angle is formed when a side of a polygon is extended outside of the shape, creating an angle between that extended line and the adjacent side. This concept plays a crucial role in understanding the properties of polygons, particularly in relation to their interior angles and overall geometry. The relationship between exterior angles and their corresponding interior angles is fundamental in calculating the total angle measures in various polygons.

5 Must Know Facts For Your Next Test

1. The measure of an exterior angle is equal to the sum of the measures of the two non-adjacent interior angles of a polygon.
2. In any polygon, the sum of all exterior angles, one at each vertex, is always $360^{\circ}$, regardless of the number of sides.
3. Exterior angles can be calculated easily by subtracting an interior angle from $180^{\circ}$ since they are supplementary.
4. For regular polygons, where all sides and angles are equal, each exterior angle can be found by dividing $360^{\circ}$ by the number of sides.
5. Understanding exterior angles helps in solving problems related to polygonal shapes, such as finding unknown angles or determining specific properties related to their geometry.

Review Questions

• How do exterior angles relate to interior angles in polygons?
  • Exterior angles have a direct relationship with interior angles in polygons. Each exterior angle is equal to the sum of the two opposite interior angles. Additionally, since each pair of interior and exterior angles at a vertex are supplementary, knowing one allows you to easily calculate the other. This relationship is fundamental when analyzing polygons and helps in solving various geometric problems.
• What is the significance of the sum of exterior angles being $360^{\circ}$ for all polygons?
  • The fact that the sum of exterior angles for any polygon is always $360^{\circ}$ highlights a consistent property across all shapes, regardless of how many sides they have. This principle simplifies calculations and provides a method for verifying results when working with complex polygons. It also reinforces the understanding that no matter how irregular a polygon may appear, this geometric truth remains constant.
• Evaluate how understanding exterior angles can enhance problem-solving skills in geometric contexts involving polygons.
  • Understanding exterior angles enhances problem-solving skills by providing tools to analyze and manipulate geometric relationships effectively. For instance, knowing that the sum of exterior angles equals $360^{\circ}$ allows for quick verification when working through problems involving unknown angles. Additionally, using exterior angles can simplify calculations in complex figures, enabling students to find solutions more intuitively and efficiently. Mastery of this concept encourages deeper reasoning about shape properties and relationships within geometry.

Related terms

Interior angle: An interior angle is formed by two adjacent sides of a polygon, situated inside the shape.

Polygon: A polygon is a closed figure composed of three or more straight sides that meet at vertices.

Sum of angles: The sum of the interior angles of a polygon can be calculated using the formula $(n-2) \times 180^{\circ}$, where n is the number of sides.