Download Exploring Angle Measure in Regular Polygons

Exploring Angle Measures of Polygons
The sum of the interior angles in a triangle is ___________.
1) a) Draw an equilateral triangle.
An equilateral
triangle is a regular
polygon.
Side lengths in your equilateral triangle ____________
b) What is the measure of each interior angle of an equilateral triangle?
2) a) Draw a square.
Side lengths in your square ____________
b) Draw a diagonal between two non-adjacent corners so the square is divided into
triangles.
c) How many triangles are created?
d) What is the sum of the interior angles of a square?
e) What is the measure of each interior angle of a square?
This means
not side by
side.
3) Repeat step 2 for a regular pentagon and a regular hexagon.
(Note: You will need to draw more than one diagonal to divide each shape into triangles.)
a) Regular Pentagon
Side lengths in your regular pentagon ____________
i. Draw a diagonal between two non-adjacent corners so the pentagon is
divided into triangles.
ii. How many triangles are created?
iii. What is the sum of the interior angles of a regular pentagon?
iv. What is the measure of each interior angle of a regular pentagon?
b) Regular Hexagon
Side lengths in your regular hexagon ____________
i.
Draw a diagonal between two non-adjacent corners so the hexagon is
divided into triangles.
ii.
How many triangles are created?
iii.
What is the sum of the interior angles of a regular hexagon?
iv.
What is the measure of each interior angle of a regular hexagon?
4) Complete the following table for the shapes that you drew from steps 1 to 3.
Figure
Equilateral triangle
Number
of Sides
Number of
Triangles
Sum of Interior
Angles
1
3
180°
Measure of Each
Interior Angle
Square
Regular pentagon
Regular hexagon
5) a) Do you notice any patterns in the table? State the patterns that you see?
b) Without making a sketch, determine the sum of the interior angles of these regular
polygons.
•
An 8 sided figure
_______________
•
A 10 sided figure
_______________
•
A 20 sided figure
_______________
c) Without making a sketch, determine the measure of each interior angle of these
regular polygons.
•
An 8 sided figure
_______________
•
A 10 sided figure
_______________
•
A 20 sided figure
_______________
d) Fill out the chart below.
Number
of Sides
Figure
Sum of Interior
Angles
Measure of Each
Interior Angle
8-sided regular polygon
10-sided regular polygon
20-sided regular polygon
e) What is the name of an 8 sided polygon?
_________________
10 sided polygon?
20 sided polygon?
_______________
______________