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ZingPath: Polygon Fundamentals

Sum of the Exterior Angles of Polygons

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Sum of the Exterior Angles of Polygons

Geometry

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The sum of the exterior angles of regular and non-regular convex polygons by shrinking the polygon is found.

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Now You Know

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

  • After completing this Activity Object, learners will be able to:
  • 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.

Example:

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 point's 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.

Exterior angles are those that are found on the outside of the 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.

Algebraic proof:

Tutorial Details

Approximate Time 15 Minutes
Pre-requisite Concepts Students should be familiar with these concepts: angles, drawing polygons, exterior angles of polygons, interior angles, polygons, and the sum of the interior angles of polygons.
Course Geometry
Type of Tutorial Visual Proof
Key Vocabulary angles, exterior angles, polygons