SOLVING PROBLEMS ON ANGLES AND SIDES OF POLYGON

Solving Problems
Involving Sides and
Angles of a Polygon

◦The learner solves problems involving sides and
angles of a polygon.
This module is designed for you to:
a. solve problems involving sides and angles of polygons; and
b. realize the importance of polygons in real-life.
Learning Competencies

TRIVIA
QUESTION
In what City can we
find the largest
church in the world?

Match column A with Column B, then write the
letter of the correct answer to each no.
◦ Column A Column B
◦ A. PENTAGON 1. 10 sides
◦ C NONAGON 2. 5 sides
◦ I . QUADRILATERAL 3. 7 sides
◦ L. TRIANGLE 4. 4 sides
◦ N. HEXAGON 5. 9 sides
◦ T. HEPTAGON 6. 5 angles
◦ V. Decagon 7. 6 sides
◦ Y. Octagon
◦ ____ ____ ____ ____ ____ ____ ____
◦ 1 2 3 4 5 6 7
◦
In what city can we find
the largest church in the
world?

◦ C. NONAGON 2. 5 sides
◦ Y. Octagon
◦ 1 2 3 4 5 6 7
V A T I C A N

◦ C. NONAGON 2. 5 sides
◦ Y. Octagon
In what city can we find
the largest church in the
world?
VATICAN CITY

VATICAN CITY
This Photo by Unknown Author is licensed under CC BY-SA
St Peter's Basilica, located in the Vatican City, is
considered one of the Catholic Church's holiest
temples and an important pilgrimage site. St.
Peter's Basilica is one of the holiest temples for
Christendom and one of the largest churches in
the world.

This
Photo
by
Unknown
Author
is
licensed
under
CC
BY-SA
Linear pairs
Two angles are said to be linear if they are adjacent angles formed by two
intersecting lines. The measure of a straight angle is 180 degrees, so a linear
pair of angles must add up to 180 degrees.
Two angles whose sum is 180°.
A + B = 180°
45° + 135° = 180°
Example:
45° 135°

Find the pair angles:
80° x
40°
y
1. 80° + x = 180°
x = 180° - 80°
x = 100°
1. 40° + y = 180°
y = 180° - 40°
y = 140°
60 seconds

This
Photo
by
Unknown
Author
is
licensed
under
CC
BY-SA
Remember:
• The word polygon is a Greek word, where poly means many
and gon means angle.
• A polygon is a flat or plane figure with at least three straight
sides and angles, and typically five or more. It does not have
curved sides.

Regular Polygons- polygons with
congruent sides.
Irregular Polygons- polygons
whose sides are not congruent.

Interior Angles-
are angles formed by the sides of a
polygon

Exterior Angles –
are angles formed where the sides of the polygon
are extended.

SUM OF ANGLES
The sum of the interior angles of a convex
polygon with n sides is given by:
S = (n – 2)180°

Example Problem :
1. Liza received a regular hexagonal jewelry storage from her mom as a
Christmas gift. If its perimeter is 120cm, what is the measure of each side of
the said storage?

Steps in solving a problem:
1. Read the problem carefully
2. Illustrate or draw
3. Identify the given.
4. Know what is ask.
5. Show your solution

Problem :
1. Liza received a regular hexagonal jewelry storage from her mom as a
Christmas gift. If its perimeter is 120cm, what is the measure of each side of
the said storage?
Solution:
Let 𝑃 = perimeter of the regular hexagon = 120 cm.
s=the measure of each side = ?
Formula: P = 6s or
S =
𝑃
6
S =
120
6
S = 20 cm
1
2
3
4
5
6

Example Problem :
2. Given the figure below, determine the unknown measure
of the exterior angle.
Solution:
100° + x° = 180°
x = 180° - 100°
x = 100°

3. Rosa was assigned to measure all the interior angles of
heptagon. What is the sum of the measures of all its interior
angles? Solution:
Let 𝑆 = the sum of the measures of all the interior angles
and 𝑛 = the number of sides of a polygon. 𝑆 =
Formula:
S= (n -2)180°
S = (7 – 2 )180°
S = 5(180°)
S = 900°
1
2
3
4
5
6
7

Problem :
4. In their Mathematics group activity, Ryan was assigned to measure the exterior angles of a
regular octagon. What is the measure of each exterior angle of a regular octagon?
Solution:
Let x = be the measure of each exterior angle
n = number of sides of a polygon = 8
Formula: Sum = (n-2)180°
Sum = (8-2)180°
= 6(180°)
= 1,080°
Interior angle= 1,080°/8
=135°
Exterior angle = 180°-135°
so, x = 45°
1
2
3
4
5
6
7
8
x

Problem
5: Given the figure below, determine the sum of the measures of the interior
angles and the value of x.
Solution:
Let 𝑆 = the sum of the measures of all the interior angles
and 𝑛 = the number of sides of a polygon. 𝑆 =
Formula:
S= ( n -2)180°
S = ( 5 – 2 )180°
S = 3( 180°)
S = 540°

Solution:
120° + 80° + 150° + x° = 540°
(120° + 80° + 150°) + x° = 540°
350° + x° = 540°
350° + x° = 540°
x° = 90°
- 350° - 350°

This Photo by Unknown Author is licensed under CC BY-SA
Your teacher gave you a 200cm wire. She asked you to make a
regular polygon out of it. Answer the following questions by
completing the table.
a. What is the measure of each side?
b. What is the sum of its interior angles?
c. What is the measure of each interior angle?
d. What is the measure of each exterior angle?
Exercise:

Table:
polygon Measure of each
sides
Sum of the
interior angle
Measure of each
interior angle
Measure of each
exterior angle
Square
pentagon
octagon

This
Photo
by
Unknown
Author
is
licensed
under
CC
BY-SA
Square- (n): 4
Measure of each side (s):
side = Perimeter/no. of sides
s = 200/4 = 50 cm
Sum of interior angles (S):
S = (n – 2)180°
S = (4-2)180°
= 2(180°)
= 360°
60
sec
Interior Angle:
360°/4 = 90°
Exterior Angle:
180° - 90° = 90°

Pentagon: (n): 5
s = 200/5 = 40 cm
S = (n – 2)180°
S = (5-2)180°
= 3(180°)
= 540°
60
sec
Exterior Angle:
180° - 108° = 72°
Interior Angle:
540°/5 = 108°

This
Photo
by
Unknown
Author
is
licensed
under
CC
BY-SA
Octagon- (n): 8
s = 200/8 = 25 cm
S = (n – 2)180°
S = (8-2)180°
= 6(180°)
= 1,080°
60
sec
Interior Angle:
1,080°/8 = 135°
Exterior Angle:
180° - 135° = 45°

MS. ARLEEN G. TONGOL
Have a Nice Day
God Bless Us
Always…

SOLVING PROBLEMS ON ANGLES AND SIDES OF POLYGON

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