Angles of Convex Polygons 
Grade: High School 
Content Area: Geometry 
Time Frame: 6090 minutes 

Unit/Lesson Overview: The purpose of this lesson is to investigate the sum of the interior and exterior angles of any convex polygon, and determine a mathematical relationship between the number of sides and the sum of the interior angles of any convex ngon.

Student Standards (TEKS)
for
explanation of a TEK, click on the TEK 
Language Arts: 

Math: 

Social Studies: 

Science: 

Technology: 

Geometry: 

Additional TEKS: 
Geometry: b2B, c1, e2B
Technology: c1, c2 

I Can.... Determine the sum of the interior angles of any convex polygon.
Determine the sum of the exterior angles of any convex polygon.
Use numeric and geometric patterns to make generalizations about the angle relationships of polygons. 
Assessment(s): None assigned.: 
TAKS Objectives:
Reading: 

Writing: 

Math: 
Obj 1; Obj 2 
Social Studies: 

Science: 


Bloom's Taxonomy
Yes 
Knowledge 
Yes 
Comprehension 
Yes 
Application 
Yes 
Analysis 
Not Chosen 
Synthesis 
Not Chosen 
Evaluation 

Big 6 Skills
Not Chosen 
Task
Definition 
Not Chosen 
Info. Seeking
Strategies 
Not Chosen 
Location and
Access 
Not Chosen 
Use of Information 
Not Chosen 
Synthesis 
Not Chosen 
Evaluation 

Supplementary Resources / Materials: Student Handout (optional)
Sketchpad file (Angles of polygons)
File: angle investigation for convex polygons.doc
File: Angles of Polygons.gsp

Internet Links:

Accommodations: 
Procedures 
Introductory Activity (WarmUp): Use the Warm Up page to review the concept of polygon figures and not polygon figures.
Define convex and nonconvex polygons using sketchpad to demonstrate the difference between the types.
Review concept of regular and nonregular polygons 
Lesson: Use the triangle sketch to investigate the relationship of the sum of all interior and exterior angles of any shape triangle, quadrilateral, pentagon, and hexagon; provide 23 minutes for each polygon and have students write down they findings for questions 14.
Have students determine the relationship between the number of sides of a polygon and the sum of the interior angles; provide about 5 minutes. Have students explain to you how they arrived to the equation, and verify it using the graphing calculator. Test their equation using their know values for pentagons, hexagons, etc.
What are the limitations of the

Reteach: In this lesson the students will need to be able to find a linear equation of a set of data. This can be done either using the graphing calculator or algebraically; preferably both.

Extension: Q5.Can you find a formula to determine the measurement of each interior angle of a regular ngon
Extension question.

Guiding Questions: Q5. Why does the sum of all the exterior angles of any convex polygon always adds to 360 degrees?
Q5. Will your results change if the polygons are regular?

Summary Questions: In your own words, describe the difference between a convex polygon and a nonconvex polygon.
Why does the sum of all exterior angles of a convex polygon always add to 360 degrees?

Reflection:
