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# ZingPath: Angles and the Pythagorean Theorem

## Sum of the Exterior Angles of Polygons                Searching for

## Angles and the Pythagorean Theorem

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### Lesson Focus

#### Sum of the Exterior Angles of Polygons

Algebra Foundations

You will find the sum of the exterior angles of convex polygons by shrinking the polygon.

### Now You Know

After completing this tutorial, you will be able to complete the following:

• Explain that the sum of the exterior angles of convex polygons is always 360°.

### Everything You'll Have Covered

All of the angles of a convex polygon measure less than 180� and all diagonals are located in the interior of it. All of the interior angles of the above polygons measure less than 180�. Note also that all diagonals are located in the interior of it.

In this Activity Object, students will create convex polygons.

A polygon with an angle measuring more than 180� is called a concave polygon. If an angle of a polygon points inward such as the one below, it measures more than 180�. Note also that not all diagonals are located in the interior of the polygon. The drawing tool in this Activity Object will not allow students to create a polygon with an angle measuring more than 180�. An angle is formed by two noncollinear rays that share the same endpoint.

Angles are measured in degrees. We use a protractor to measure angles. Interior angles are those that are formed in the inside of a polygon.  The sum of the exterior angles of convex polygons is 360�.

The sum of the exterior angles for each polygon is consistent for all types of polygons whether they are regular or irregular, large or small -- no matter how many sides. The sum is always 360�.

Geometric proof:

When all of the angles of a convex polygon converge, or pushed together, they form one angle called a perigon angle, which measures 360 degrees. If the sides of the convex polygon are increased or decreased, the sum of all of the exterior angle is still 360 degrees. More sides can be added to the polygon and they will still form a perigon angle. Therefore, the number of sides does not change the sum of the exterior angles of a convex polygon.  ### Tutorial Details

 Approximate Time 20 Minutes Pre-requisite Concepts Learners should be familiar with angles, drawing polygons, exterior angles of polygons, interior angles, polygons, and the sum of interior angles of polygons. Course Algebra Foundations Type of Tutorial Visual Proof Key Vocabulary angles, exterior angles, polygons