Interior And Exterior Angles Of Polygons Worksheet With Answers Pdf
Geometry is one of the most important branches of mathematics since it deals with the study of shapes, sizes, and positions of objects. One of the topics in geometry is polygons. A polygon is a closed plane figure that is bounded by straight lines. Polygons can have different shapes and sizes, and they also have different types of angles. Understanding the different types of angles in a polygon is important in solving problems related to polygons. In this article, we will discuss the interior and exterior angles of polygons and provide a worksheet with answers in pdf format.
Interior Angles of Polygons
Interior angles are angles that are inside a polygon. The sum of the interior angles of a polygon is given by the formula: (n-2) x 180 degrees, where n is the number of sides of the polygon. For example, a triangle has three sides, so the sum of its interior angles is (3-2) x 180 = 180 degrees. A square has four sides, so the sum of its interior angles is (4-2) x 180 = 360 degrees.
In addition to the sum of the interior angles formula, there is also a formula for calculating the measure of each interior angle in a regular polygon. A regular polygon is a polygon that has all sides and angles equal. The measure of each interior angle in a regular polygon is given by the formula: (n-2) x 180 / n degrees, where n is the number of sides of the polygon. For example, the measure of each interior angle in a regular hexagon (a polygon with six sides) is (6-2) x 180 / 6 = 120 degrees.
Exterior Angles of Polygons
Exterior angles are angles that are outside a polygon. The measure of each exterior angle of a polygon is equal to 360 / n degrees, where n is the number of sides of the polygon. For example, each exterior angle of a regular pentagon (a polygon with five sides) is 360 / 5 = 72 degrees.
In addition to the measure of exterior angles, there is also a formula for calculating the sum of the exterior angles of a polygon. The sum of the exterior angles of a polygon is always equal to 360 degrees. This formula is useful in solving problems related to polygons.
Worksheet with Answers in Pdf Format
Now that we have discussed the interior and exterior angles of polygons, it is time to test your knowledge. We have provided a worksheet with answers in pdf format that you can download and use to practice solving problems related to polygons. The worksheet contains different types of problems and their solutions.
To download the worksheet with answers in pdf format, click on the following link:
https://www.mathwarehouse.com/polygons/interior-and-exterior-angles-worksheet-with-answers.pdf
Conclusion
In conclusion, understanding the interior and exterior angles of polygons is important in solving problems related to polygons. The sum of the interior angles of a polygon is given by the formula (n-2) x 180 degrees, while the measure of each interior angle in a regular polygon is given by (n-2) x 180 / n degrees. The measure of each exterior angle of a polygon is equal to 360 / n degrees, and the sum of the exterior angles of a polygon is always equal to 360 degrees. To practice solving problems related to polygons, download the worksheet with answers in pdf format that we have provided. With practice and understanding, you will be able to solve problems related to polygons with ease.
