This document contains a strategic intervention material (SIM) for learning about the sum of interior angles of polygons. The SIM includes instructions for use, the purpose of the SIM, activities to complete with answer keys, and reference materials. The activities guide the student to determine the number of triangles formed by diagonals of different polygons and use this to calculate the sum of interior angles for triangles through octagons.

1. 1
STRATEGIC
INTERVENTION
MATERIAL

2. 2
Prepared by:
Asakil, Flordeliza V.
Casumbal, Epifania J.
Dela Cruz, Lorena O.
Pagulayan, Rowena H.
Reluba, Ma. Theresa C.
Unida, Francisca R.
RIZAL HIGH SCHOOL
SY 2011 - 2012
2

3. 3
How to use this Strategic Intervention Material (SIM)?
• Keep this material neat and clean.
• Thoroughly read every page.
• Follow carefully all instructions indicated in every activity.
• Answer all questions independently and honestly.
• Write all your answers on a sheet of paper.
• Be sure to compare your answers to the KEY TO CORRECTIONS only
after you have answered the given tasks.
• If you have questions or clarifications ask your teacher.
Purpose of Strategic Intervention Material (SIM)
This learning package is intended to supplement your
classroom learning while working independently . The activities
and exercises will widen your understanding of the different
concepts you should learn.

4. 4
Honey, I
shrunk the
kids !!!
Title Card
Topic: SUM OF INTERIOR
ANGLES OF POLYGON

5. 5
Do you want to know
how the kids got
shrunk ?
Are you kind enough
to help them regain
their normal self ?

6. 6
Thank you. I know
you are more than
willing to help.
Sit tight and let’s try to do
the following activities so
that we can unfold their
story.

7. 7
Polygon No. of Sides No. of
Triangles
Sum of
Interior
Angles
Triangle
Fill up the table as you follow the instructions:
R
P
R
1
2
3
S
S
1 2 3
R
N M
S
1
2 3
N M
P
P
Activity 2
Guide Card
• Do this paper-folding activity using a cutout of a triangle.
• Name the triangle RPS and label the corresponding ∠1,
∠ 2, and ∠ 3 as shown in the figure.
• Fold the triangle so that the point P lies on RS forming a
trapezoid RNMS.
• Fold again so that the vertices R and S meet at point P.
• Determine the sum of the measure of the marked angles
1, 2, and 3.
• Verify your answer by using a protractor.
• Therefore, the sum of the measure of the interior angles of
any triangle is _____ .
Activity 1

8. 8
Polygon No. of Sides No. of
Triangles
Sum of
Interior
Angles
Triangle 3 1 1800
Quadrilateral
A D
O
R
• Draw all possible diagonals from one
vertex. (e.g. from vertex A)
How many diagonals are possible?
From that possible diagonal/s, how many
triangles are formed?
Take note that the sum of the interior
angles of a triangle is 180º.
The measure of angles 1 + 2 + 3 = 1800
Activity 3
An apple
helps you to
concentrate.
1
2
3

9. 9
Polygon No. of Sides No. of
Triangles
Sum of
Interior
Angles
Triangle 3 1 1800
Quadrilateral 4 2 3600
Pentagon
P
D
R
E
O
• Draw all possible diagonals
from one vertex. (e.g. vertex E)
How many diagonals are
possible?
From that possible diagonal/s,
how many triangles are formed?
A D
O
R
Since there are two triangles formed, therefore
the sum of the interior angles of a quadrilateral is
3600. Hence, 2(1800)=3600.
Activity 4
I’m an angel
in disguise. I
can help you.

10. 10
P
D
R
E
O
Therefore, the measure of angles
P+E+D+R+O=5400.
Oh my God !
Now I know.

11. 11
Polygon No. of Sides No. of
Triangles
Sum of Interior
Angles
Triangle 3 1 1(1800)=1800
Quadrilateral 4 2 2(1800)=3600
Pentagon 5 3 3(1800)=5400
Hexagon
Heptagon
Octagon
Nonagon
n - gon n n - 2
To check your
answer go to
page 18
The first 3 steps has already
done for you. Follow the same
procedure to complete the
table.
Activity 5

12. 12
The couple Poly and Gonny have five nice but
smart kids namely, Trigie, Quadie, Pengie, Hexie, and
Heptie. Mr. Poly is working on an experiment so he
prohibits his siblings to enter a room, where he keeps a
machine which he hopes can transform bigger objects to
smaller once or vice-versa. The kids are so eager and
curious to see the machine which for them can do
magic.
One day, when Mr. Poly is at work and Mrs.
Gonny goes to market, the kids agreed to enter the room
to satisfy their curiosity. Later, the mother came. Finding
the kids nowhere, she proceeded to the laboratory room
and accidentally push a button. A spark of bright light
suddenly appeared. Mrs. Gonny almost lost her
consciousness and shouted “Honey, I shrunk the kids.”
To help the kids regain their normal size you need to
answer the subsequent questions appropriately. For
every correct answer one of the kids will grow back
to its normal size.
The Story Behind…

13. 13
1. Find the sum of the interior angles of a 32-gon.
4. The sum of the measure of the interior angles of a polygon is
known to be between 2100 and 2200. How many sides does the
polygon have?
5. In a pentagon PQRST, the measure of angle P is 600, angle
Q is 1300,angle S and T are each 3 times as large as angle R.
Find the measure of angle R, S, and T.
ACTIVITY CARD
To check your
answer go to
page 19
2. The face of a honeycomb consist of interlocking
regular hexagon. What is the measure of each angle of
these hexagons?
3. A soldier’s badge is in the form of a pentagon
with 3 right angles. The other two angles are
congruent. Find their measure.

14. 14
Congratulations !
You will receive a
reward for your
help.
To claim your
prize you must
proceed to the
next activity.
Just turn to
next page.

15. 15
ASSESSMENT CARD
Solve the ff. problems. Write the
letter of the correct answer in each
box at the bottom that contains the
item number.
1. Sum of interior angles of undecagon.
2. Numbers of triangles formed from just
one vertex of 13-gon.
3. Size of each angle of a regular
decagon.
4. No. of sides of n-gon with the sum of
the interior angles 9000.
5. Sum of interior angles of a 30-gon.
6. The no. of sides of a polygon with
1560 each angle.
7. Sum of the interior angles of a
polygon with 1600 each angle.
L 11
S 24
G 15
P 7
F 144
D 5040
R 12
O 2880
T 1620
4 7 1 7 3 6 7 2 5
To check your
answer go to
page 20

16. 16
ENRICHMENT CARD
1. Find the sum of the interior angles of
the given polygon if the polygon can be
bisected.
2. Given: ABCDE is a regular pentagon.
Find: a.) the sum of the measure of
angle P, Q, R, S, T.
b.) the measure of each
angle in letter a.
B
C
D
F
E
A
D
C
B
A
E
T
S
R
Q
P
To check your
answer go to
page 21

17. 17
http://www.youtube.com/watch?v=JtPK8XezY
PM&feature=related
http://www.youtube.com/watch?v=ZaSjlF4y
BRg&feature=relmfu
http://www.cliffsnotes.com/study_guide/Angle-
Sum-of-Polygons.topicArticleId-18851,articleId-
18794.html
http://www.mathwarehouse.com/geometry/poly
gon/
REFERENCE CARD
Polygons, Geometry (Prentice Hall)
by Bass, Hall, Johnson,Wood, pp.
68-72
Polygons, Geometry by Miftlin, pp.
101-105
Angle Measure of a Triangle,
Geometry by Bernabe, pp. 19-20
Related Topics:
Angle Sum Theorem, Mathematics
(Prentice Hall) by Bass, Charles,
Johnson, Kennedy, pp. 145-150
Polygons, Laidlaw Geometry by Travers,
Dalton, Layton, pp. 460-465

18. 18
KEY TO CORRECTIONS
ANSWER CARD
Polygon No. of Sides No. of
Triangles
Sum of
Interior
Angles
Triangle 3 1 1(1800)=1800
Quadrilateral 4 2 2(1800)=3600
Pentagon 5 3 3(1800)=5400
Hexagon 6 4 4(1800)=7200
Heptagon 7 5 5(1800)=9000
Octagon 8 6 6(1800)=10800
Nonagon 9 7 7(1800)=12600
n - gon n n - 2 (n – 2)1800
ACTIVITY 5
Brilliant
Perfect Score
If you get …
10 - 12
7 - 9
6 and below
Start all over
again.
Note: If you are not yet satisfied with your work, you can always go back.

19. 19
ACTIVITY CARD
1. 54000
2. 1200
3. 1350
4. 14
5. angle R = 500,
angle S=1500,
angle T=1500
KEY TO CORRECTIONS
ANSWER CARD
Perfect Score
5 - 6
4
3 and below Start all over
again.
If you get …
Note: If you are not yet satisfied with your work, you can always go back.
Brilliant

20. 20
ASSESSMENT CARD
POT OF GOLD (7 points)
KEY TO CORRECTIONS
ANSWER CARD
Start all over
again.
If you get …
Note: If you are not yet satisfied with your work, you can always go back.
Brilliant
Perfect Score
5 - 6
4
3 and below

21. 21
KEY TO CORRECTIONS
ANSWER CARD
Start all over
again.
If you get …
Note: If you are not yet satisfied with your work, you can always go back.
Brilliant
Perfect Score
2
0 - 1
ENRICHMENT CARD
1. 7200
2. a.) 1800
b.) 360