The Mystery of
Angles and Polygons
BY MRS. THIESSEN
Chapter One
Once upon a time on a dark and lonely
night, I came upon a regular polygon. I
wasn’t sure who he was until the light
reflected on his face. Not seen in months,
the nonagon has reappeared. How did I
know it was the nonagon ?
To help solve the mystery
copy this list of polygon names and their
number of sides. Put them to memory.
triangle - 3
quadrilateral - 4
pentagon - 5
hexagon - 6
heptagon - 7
octagon - 8
nonagon - 9
decagon - 10
undecagon - 11
dodecagon - 12
CSI at work
What do we really know about.........
Mr. Nonagon
How many sides does
he have ?
How many angles
does he have ?
How many wives
does he have ?
nine
nine
?
Chapter Two
What is the angle of his crime ?
CSI - back again
In order to determine Mr. Nonagon s angle use the following formula :
(and keep it a secret )
180º (N-2)
N being the number of sides
So, let’s calculate . . .
Mr. Nonagon has 9 angles
• and we need to use the
formula 180º (N - 2)
• we need to substitute
9 (angles) for the “n”
180º (N-2)
becomes
180º (9-2)
SO LET’S SOLVE THE PROBLEM
9-2 = 7
AND
180 X 7 =1260 º
MR. NONAGON IS 1260º
So, the clues are
starting to add up
to a picture of
Mr. Nonagon
All nine of his angles
add up to 1260º
Final Chapter
It occurred to me that Mr. Nonagon may
have been recognized due to the angle over
his right eye. I wonder how we can
figure out the measure of this angle ???
CSI - BACK TO THE BASICS
WHAT DO WE
ALREADY
KNOW ?
all nine angles
add up to
1260º
HOW CAN I FIND THE
MEASURE OF
JUST ONE ANGLE ?
I GOT IT !!
DIVIDE 1260 º
BY 9
1260 ÷ 9 =
140 º
CONCLUSION
MR. NONAGON CAN TRY TO HIDE,
BUT WE WILL ALWAYS RECOGNIZE
HIM BY HIS ANGLES.
THIS STORY WAS
CREATED ESPECIALLY
FOR EXPLORER
STUDENTS.
HOMEWORK
REGULAR SIDES /
180(N-2) POLYGON ANGLES TRIANGLE
QUADRILATERAL
PENTAGON
HEXAGON
HEPTAGON
OCTAGON
NONAGON
DECAGON
UNDECAGON
DODECAGON
INTERIOR EXTERIOR
ANGLE ANGLE