Introduction

Interior and exterior angle calculations are crucial in geometry. They are important in measuring the angles of shapes and structures, whether they are two-dimensional or three-dimensional. In this article, we will delve into lesson 71 of interior and exterior angles and its answer key.

The Basics

Before we dive deeper, let us review the basics. Interior angles are angles found inside a shape, while exterior angles are angles formed outside a shape. When we add the interior and exterior angles of a shape, we get 360 degrees. This is a fundamental rule in geometry.

The Lesson 71

Lesson 71 focuses on the relationship between interior and exterior angles of polygons. It teaches us how to calculate the interior and exterior angles of a polygon with n sides. We can use the formula: Interior angle = (n-2) x 180 / n Exterior angle = 360 / n

Answer Key

Now, let us proceed to the answer key of lesson 71. Here are some examples: 1. Find the interior and exterior angles of a hexagon. Interior angle = (6-2) x 180 / 6 = 120 degrees Exterior angle = 360 / 6 = 60 degrees 2. Find the interior and exterior angles of a decagon. Interior angle = (10-2) x 180 / 10 = 144 degrees Exterior angle = 360 / 10 = 36 degrees 3. Find the interior and exterior angles of a pentagon. Interior angle = (5-2) x 180 / 5 = 108 degrees Exterior angle = 360 / 5 = 72 degrees

Applications

The knowledge of interior and exterior angles is applicable in various fields. Architects and engineers use these calculations in designing structures such as buildings, bridges, and roads. These angles are also important in computer graphics for creating 3D models and animations.

Conclusion

In conclusion, lesson 71 of interior and exterior angles is essential in geometry. It helps us understand the relationship between the angles of polygons and their properties. With this knowledge, we can solve problems involving angles and apply them in various fields.