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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. Vertex - point where two sides meet. Two or more of these points are called vertices.

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exercises
EXERCISES
  • TELL WHETHER OR NOT EACH OF THE FOLLOWING IS A POLYGON.
exercises1
Exercises
  • TELL WHETHER A POLYGON IS CONVEX OR NOT.
polygon parts1
POLYGON PARTS

Vertex - point where two sides meet. Two or more of these points are called vertices.

Side - one of the line segments that make up the polygon.

polygon parts2
POLYGON PARTS

Diagonal - a line connecting two vertices that isn't a side.

examples
Examples:

Solutions:

a. Sa = (n – 2) 180⁰

= (11 – 2) 180⁰

= 9(180⁰)

= 1620⁰

  • 1. What is the sum of the measures of the interior angles of a convex polygon with
  • a. 11 sides
  • b. 15 sides
examples1
Examples:

Solutions:

b. Sa = (n – 2) 180 ⁰

= (15 – 2) 180⁰

= 13(180⁰)

= 2340⁰

  • 1. What is the sum of the measures of the interior angles of a convex polygon with
  • a. 11 sides
  • b. 15 sides
examples2
Examples:

Solutions:

b. Sa = (n – 2) 180⁰

= (7 – 2) 180 ⁰

= 5(180 ⁰)

S = 900⁰

  • 2. Find the sum of the measures of the interior angles of a convex heptagon.
examples3
Examples:

Solutions:

b. Sa = (n – 2) 180⁰

1440⁰ = (n – 2) 180⁰

1440 = 180⁰ n – 360⁰

n =

n =

n = 10

  • 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.

slide14
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

slide15
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

a find the sum of the measures of the vertex angles for each polygon
A. FIND THE SUM OF THE MEASURES OF THE VERTEX ANGLES FOR EACH POLYGON

15-gon

50- gon

35-gon

slide18
B. FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN

1260°

1620°

polygon parts3
POLYGON PARTS

Exterior Angle - Angle formed by two adjacent sides outside the polygon.

Interior Angle - Angle formed by two adjacent sides inside the polygon.

investigate
Investigate
  • 1, 2 and 3 are interior angles.
  • 4,5 and 6 are exterior angles
  • 1 + 4 = 180°
  • 2 + 5 = 180°
  • 3 + 6 = 180°

6

3

1

1

2

5

4

slide23
If m1= 70, what is the measure 4?
  • m4= 110
  • If m2 = 80, what is the m5?
  • m5= 100
  • If m3 = 30, what is the m6?
  • m6= 150

6

3

1

1

2

5

4

the sum of the exterior angles of an n gon is 360
The sum of the exterior angles of an n-gon is 360°
  • m4= 110
  • m5= 100
  • m6= 150
  • m2 + m4 + m6=360

6

3

1

1

2

5

4

slide25
20°

160°

110°

70°

70°

110°

60°

120°

120°

60°

60° + 60 ° + 110 ° + 20 ° + 110° = 360°

examples4
Examples:

Solution:

Ea =

Ea =

= 60

  • 1. How many degrees are there in each of the exterior angle of a regular hexagon?
find the number of sides of a regular polygon when the measure of the exterior angl e is given
FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE MEASURE OF THE EXTERIOR ANGL E IS GIVEN

30°

10°

slide30
FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN

1980°

4320°

find the number of sides of a regular polygon when the measure of the exterior angle is given
FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE MEASURE OF THE EXTERIOR ANGLE IS GIVEN

24°

45°

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