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Introduction

Geometry is a branch of mathematics that deals with the study of shapes and their properties. One of the most important concepts in geometry is the concept of angles. An angle is formed by two rays that have a common endpoint called the vertex. The exterior angle of a polygon is an important concept in geometry that is used to describe the angle formed by a line that extends outside the polygon. In this article, we will discuss the definition of an exterior angle, its properties, and how to calculate it.

Definition of Exterior Angle

An exterior angle of a polygon is an angle formed by a side of the polygon and the extension of an adjacent side. In other words, if a polygon has n sides, then it has n exterior angles, each of which is formed by a side of the polygon and the extension of an adjacent side. The sum of all the exterior angles of a polygon is equal to 360 degrees.

Properties of Exterior Angles

• An exterior angle of a polygon is greater than either of the two adjacent interior angles.
• The sum of an exterior angle and its adjacent interior angle is equal to 180 degrees.
• The sum of all exterior angles of a polygon is equal to 360 degrees.

Examples of Exterior Angles

• In a triangle, each exterior angle is equal to the sum of the two opposite interior angles.
• In a quadrilateral, the sum of all exterior angles is equal to 360 degrees.
• In a regular polygon, each exterior angle is equal to the same value.
• In a pentagon, each exterior angle is equal to 72 degrees.
• In a hexagon, each exterior angle is equal to 60 degrees.
• In an octagon, each exterior angle is equal to 45 degrees.
• In a nonagon, each exterior angle is equal to 40 degrees.
• In a decagon, each exterior angle is equal to 36 degrees.
• In a dodecagon, each exterior angle is equal to 30 degrees.
• In a 20-sided polygon, each exterior angle is equal to 18 degrees.

FAQs

• What is the relationship between an exterior angle and an interior angle of a polygon? The sum of an exterior angle and its adjacent interior angle is equal to 180 degrees.
• What is the sum of all exterior angles of a polygon? The sum of all exterior angles of a polygon is equal to 360 degrees.
• How do you calculate the measure of an exterior angle of a regular polygon? The measure of an exterior angle of a regular polygon can be calculated by dividing 360 degrees by the number of sides of the polygon.
• What is the measure of an exterior angle of a pentagon? Each exterior angle of a pentagon is equal to 72 degrees.
• What is the measure of an exterior angle of a dodecagon? Each exterior angle of a dodecagon is equal to 30 degrees.

Quiz

1. What is an exterior angle of a polygon?
2. What is the sum of all exterior angles of a polygon?
3. What is the relationship between an exterior angle and its adjacent interior angle?
4. How do you calculate the measure of an exterior angle of a regular polygon?
5. What is the measure of each exterior angle of a hexagon?
6. What is the measure of each exterior angle of a nonagon?
7. What is the measure of each exterior angle of an octagon?
8. What is the measure of each exterior angle of a 20-sided polygon?
9. What is the measure of each exterior angle of a quadrilateral?
10. What is the measure of each exterior angle of a triangle?

Conclusion

In conclusion, exterior angles are an important concept in geometry that help us understand the angles formed by a polygon and its surrounding space. They have properties that make them useful in solving geometric problems, such as finding the measures of interior angles or identifying the type of polygon. The sum of all exterior angles of a polygon is always 360 degrees, which is a useful fact to keep in mind when working with polygons.

In order to calculate the measure of an exterior angle of a regular polygon, we simply need to divide 360 degrees by the number of sides of the polygon. For example, in a hexagon, the measure of each exterior angle is equal to 360 degrees divided by 6, which is 60 degrees.

Overall, understanding exterior angles is an important part of mastering geometry. By knowing their definition, properties, and how to calculate them, we can better understand the shapes around us and use this knowledge to solve real-world problems.