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Sum of Angles in Polygons

Sum of Angles in Polygons

Author: Alex G

By the end of this packet you should be able to:
* compute the sum of the interior angles of any convex polygon.
* compute the measure of a single interior angle of any regular polygon.
* compute the sum of the exterior angles of any convex polygon
* find the measure of one exterior angle of a regular polygon
* compute the number of sides of a regular polygon given the measure of one angle of the polygon.

You will be able to define and use the following terms:
*regular polygon
*exterior angle
*interior angle

This packet provides a vocabulary lesson, and concept development lesson, and four practice problems for the user.

Cover art of mosaic tiles was taken from the Morgue File website which grants permission for use of its images.

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Polygon Vocabulary

Presents a few terms you will need for the lesson

Sum of Angles in a Polygon

A video discussing the sum of the interior and exterior angles in a polygon.

Helpful Hints

  1. Use exterior angles to your advantage.  It's almost always easier to work with the exterior angle formula for regular polygons.  Since exterior angle and interior angle pairs are supplementary, you can figure out the interior angle from the exterior angle.
  2. Do a sanity check on your answer. The most common mistake I see is that a single interior angle is 180 degrees.  This makes no sense visually, so think before you answer.
  3. If you don't want to memorize the interior angle formula, then understand where it comes from.  You can always cut your shape into triangles and multiply the number of triangles by 180 degrees.  
  4. It doesn't matter how many sides you have when you're finding the sum of the exterior angles.  Exterior angles always sum to 360 degrees, no matter the number of sides.

Two Examples

Step-by-step explanation of two examples.

Practice Problems

Four application problems using sums of angles in polygons

Source: photo of stop sign is clip art from Microsoft.