Worksheet: Sum of the angles of a polygon
Objective:
Students will be looking for patterns and analyze the number of sides and triangles in each polygon to derive
formulas to find the sum of interior angles and exterior angles of any polygon. They also come up with formulas
to find measure of each interior angle in a regular polygon.
Materials:
• Papers, pencils, rulers
• activity handouts
• poster
Procedure:
I.
Triangulate each polygon. That means divide each polygon into non-overlapping triangles.
II.
Use the triangle sum theorem to find the sum of interior angles of the polygons. Then fill in your
answers in the table below.
III.
Then answer all the following questions.
n
Number of sides
Number of
triangles (after
triangulating the
polygon)
Sum of the
interior angles of
the polygon
Each interior
angle of regular
polygon
Each exterior
angle of regular
polygon
Sum of the
exterior
1. Consider the interior angles of a polygon, and the exterior angles. What is the relationship between them?
2. As the number of sides of the polygon increases, what effect does this have on
a) the interior angles
b) the exterior angles
c) the sum of the interior angles
d) the sum of the exterior angles?
3. Do any of these quantities remain constant? Why? Which increase? Which decrease? Why?
4. What do you think about the formula to find the sum of interior angles of a irregular polygon? Would it be
the same? Why?