EXERCISES
• TELL WHETHER OR NOT EACH OF
THE FOLLOWING IS A POLYGON.
Exercises
• TELL WHETHER A POLYGON IS
CONVEX OR NOT.
POLYGONS
and its parts
Review
POLYGON PARTS
POLYGON PARTS
Side -- point
one
Vertex
where
of
the two
line
sides
meet.
segments
Two or more
that make
of these points
up
the
are called
polygon.
vertices.
POLYGON PARTS
Diagonal - a
line
connecting
two vertices
that isn't a
side.
ANGLE SUM MEASURES
Angle Sum measure of the
interior angles of a polygon
Polygon
No. of sides
No. of nonoverlapping
diagonals
No. of
Triangles
formed
Angle Sum
measure
triangle
3
0
1
1 x 180°or
180°
Quadrilateral
4
1
2
2 x 180°or
360°
Pentagon
5
2
3
3 x 180°or
540°
N- gon
n
n-3
n-2
(n-2)180°
Examples:
Solutions:
a. Sa = (n – 2) 180⁰
measures of the interior
= (11 – 2) 180⁰
angles of a convex polygon
with
= 9(180⁰)
 a. 11 sides
= 1620⁰
 b. 15 sides
 1. What is the sum of the
Examples:
Solutions:
b. Sa = (n – 2) 180 ⁰
measures of the interior
= (15 – 2) 180⁰
angles of a convex polygon
= 13(180⁰)
with
= 2340⁰
 a. 11 sides
 1. What is the sum of the
 b. 15 sides
Examples:
 2. Find the sum of the
measures of the interior
angles of a convex
heptagon.
Solutions:
b. Sa = (n – 2) 180⁰
= (7 – 2) 180 ⁰
= 5(180 ⁰)
S = 900⁰
Examples:
 3. How many sides
does a convex polygon
have if the sum of the
measures of its interior
angles is 1440⁰?
The polygon has
10 sides.
Solutions:
b. Sa = (n – 2) 180⁰
1440⁰ = (n – 2) 180⁰
1440 = 180⁰ n – 360⁰
n = 1440  360
180
1800
n=
180
n = 10
FIND THE NUMBER OF SIDES OF A REGULAR
POLYGON WHEN THE SUM OF THE MEASURES
OF THE VERTEX ANGLES IS GIVEN
4. 1260°
S=(n-2)180
1260 =180n-360
1260+360= 180n
1620 = 180n
n= 9
FIND THE NUMBER OF SIDES OF A REGULAR
POLYGON WHEN THE SUM OF THE MEASURES
OF THE VERTEX ANGLES IS GIVEN
4. 1260°
n =(S180) + 2
= (1260  180) + 2
=7+2
n= 9
QUIZ
A. FIND THE SUM OF THE
MEASURES OF THE VERTEX
ANGLES FOR EACH POLYGON
1. 15-gon
2. 50- gon
3. 35-gon
B. FIND THE NUMBER OF SIDES
OF A REGULAR POLYGON WHEN
THE SUM OF THE MEASURES OF
THE VERTEX ANGLES IS GIVEN
1. 1260°
2. 1620°
Angle Sum
Measures of the
Exterior Angles
of a Polygon
LESSON 7
POLYGON PARTS
Exterior
Interior
Angle - Angle
formed by
two adjacent
sides
sidesoutside
inside
the polygon.
Investigate
 1, 2 and 3 are
6
interior angles.
3
 4,5 and 6 are
exterior angles
 1 + 4 = 180°
 2 + 5 = 180°
 3 + 6 = 180°
1
4
2
5
 If m1= 70, what is the
measure 4?
6
 m4= 110
3
 If m2 = 80, what is the
m5?
 m5= 100
 If m3 = 30, what is the
m6?
 m6= 150
1
4
2
5
The sum of the exterior
angles of an n-gon is 360°
m4= 110
 m5= 100
6
3
 m6= 150
1
 m2 + m4 + m6=360
4
2
5
20°
160°
110°
70°
70°
110°
60°
120°
120°
60°
60° + 60 ° + 110 ° + 20 ° + 110° = 360°
Angle Sum measure of the
exterior angles of a polygon
Polygon
No. of
sides
Angle
Sum
measure
(interior
angles)
Measure
of EACH
INTERIOR
angle of
a regular
n-gon
Angle
Sum
measure
(exterior
angles)
Measure
of EACH
exterior
angle of
a regular
n-gon
triangle
3
1 x 180°or
180°
180°
3
360°
360°
3
Quadrilat
eral
4
2 x 180°or
360°
360°
4
360°
360°
4
Pentagon
5
3 x 180°or
540°
540°
5
360°
360°
5
N- gon
n
(n-2)180°
(n-2)180°
n
360°
360°
n
Examples:
 1. How many degrees
are there in each of the
exterior angle of a
regular hexagon?
Solution:
360
Ea =
n
Ea =
360
6
= 60
FIND THE NUMBER OF SIDES OF A
REGULAR POLYGON WHEN THE
MEASURE OF THE EXTERIOR ANGL E
IS GIVEN
1. 30°
2. 10°
QUIZ
FIND THE NUMBER OF SIDES OF
A REGULAR POLYGON WHEN THE
SUM OF THE MEASURES OF THE
VERTEX ANGLES IS GIVEN
1.1980°
2.4320°
FIND THE NUMBER OF SIDES OF A
REGULAR POLYGON WHEN THE
MEASURE OF THE EXTERIOR ANGLE
IS GIVEN
1.24°
2.45°