The Angles of a
Polygon
Lesson Plan
Course:
Math A
Unit: Study of Polygons
Lesson Title:
Angles of a Polygon
Description: Students
will learn what a polygon is, along with the difference between regular
and irregular polygons. Students will learn rules for determining
the sum of the interior angles of any polygon and for determining the
measure of each exterior angle in a regular polygon. Students will
take the information they have learned and complete practice assignments
along with a final assessment.
Learner Characteristics and Context: This is an online
multimedia supported lesson for ninth grade students. This lesson is
designed for students who have some familiarity with basic geometric
concepts and angle measurement.
Objectives:
 After
completing the lesson the student will be able to:
 Define
polygon;

Explain the difference between regular and irregular polygons;
 State the rule
for determining the sum of the interior angles of any polygon;
 Apply the rule
to any polygon;
 Draw an
exterior angle of a regular polygon;
 State the rule
for determining the measure of each exterior angle of a regular
polygon;
 Apply the rule
to any regular polygon.
Related
Standards:
New York State Math Standards
Students
will: understand mathematics and become mathematically confident
by communicating and reasoning mathematically, by applying mathematics in
realworld settings, and by solving problems through the integrated study
of number systems, geometry, algebra, data analysis, probability, and
trigonometry.
Examination Standards for State Math A Exam
4.13 sum of interior angles of a polygon
4.14 sum of exterior angles of a polygon
Timeline:
This lesson should be completed in two class periods (45 minutes each),
given one computer per student is available. This includes all
assessments. Part of a third class will be dedicated to large group
discussion of the lesson.
Learning
Activities:
 In this lesson the student will:
 Read definitions and
view examples to learn the difference between regular and irregular
polygons;
 Complete a quiz about regular and
irregular polygons (to be downloaded and turned in);
 View a presentation that
shows them how the rule for determining the sum of the interior angles
is derived along with examples for using the rule;
 Work through practice exercises
involving the interior angles of polygons;
 View
another presentation in
which students will see how to draw an exterior angle and then learn
the rule for determining the measure of each exterior angle in a
regular polygon;
 Work through practice exercises
involving the exterior angles of polygons;
 Complete
a final assessment covering all objectives (to be downloaded and
turned in).
Materials:
 The lesson will be made available
online.
 Computer and Internet access for each
student. The computers must have Microsoft Word and Microsoft
PowerPoint installed. A printer must be connected to each
computer.
Instructional Message Descriptions:
Objectives &
Instructional Message Descriptions 
Multimedia Representations 
1

Define
polygon:
Define what a polygon is and identify
the characteristics. 
Text is used for the definitions.
Images are used to show examples of polygons throughout the background
of the site. 
2

Explain the difference between regular and irregular polygons:
Describe the
difference between regular and irregular polygons. 
Text is used for the definitions.
Images are used to compare regular and irregular polygons. 
3

State the rule for
determining the sum of the interior angles of any polygon:
Derive the rule and explain what the
variable represents. 
A presentation containing text, images,
animation and audio is used to derive the rule and show how it is
used. 
4

Apply the rule
to any polygon:
Apply the rule to an irregular polygon
by inputting the number of sides to get the angle measure. 
An example of applying the rule is shown
in the presentation mentioned in #3. Text is used to provide
practice exercises. 
5

Draw an exterior
angle of a regular polygon:
Demonstrate how to draw an exterior
angle. 
A presentation containing text, images,
animation and audio is used to show how an exterior angle is drawn. 
6

State the rule for
determining the measure of each exterior angle of a regular polygon:
Give the rule and explain what the variable represents. 
The presentation, mentioned in #5, gives
the rule and shows how it is applied to regular polygons. 
7

Apply the rule
to any regular polygon:
Give a polygon and
input the number of sides to get the total exterior angle sum. 
Text is used to provide practice
exercises. The presentation, mentioned in #5, also demonstrates
examples. 
Assessment: Students will submit both their polygon quiz
and final assessment.
References:
Dressler I., & Keenan
E. (2002). Mathematics A. New York: AMSCO School
Publications, Inc.
Murray, M. (1999).
Sum of interior and exterior angles of polygons. Oswego City School
District Regents Exam Prep. Retrieved July 26, 2004, from:
http://www.regentsprep.org
