Unit 5
Notes – ​
Interior Angles of a Regular Polygon
● Define a ​
Regular Polygon​
: ____________________________________
_______________________________________________________________
● Classify 9 Types of Regular Polygons
_________
_________
_________
_________
_________
_________
_________
_________
_________
● Define a ​
Diagonal​
: __________________________________________
In the following shapes, choose a vertex to start. Connect it to as many other
vertices as possible by drawing diagonals without crossing.
a. State the number of triangles created and the number of sides for each
polygon.
a. Determine the sum of the interior angles by using interior angles of each
triangle.
1.
2.
3.
_____sides
_____sides
_____sides
_____triangles
_____triangles
_____triangles
Angle sum =_______
Angle sum =_______
Angle sum =_______
● State the ​
Angle Sum Theorem for Any Regular Polygon
● Find the sum of the measures of the interior angles of any regular
polygon.
EX) Find the sum of the interior angles of an Octagon.
EX) Classify the type of regular polygon with a sum of interior angles equal
to 1440° .
● Find the measure of an interior angle in any regular polygon.
STEPS:
1. Find the sum of the interior angles.
2. Divide the sum by the number of angles/sides (​
n​
).
(n − 2) • 180
n
= EX) Find the measure of an interior angle in a regular Hexagon.
EX) Classify the type of regular polygon with an interior angle measuring 108°.