EXERCISES

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# EXERCISES - PowerPoint PPT Presentation

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
• 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

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 PARTS

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

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
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
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.
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.

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

A. FIND THE SUM OF THE MEASURES OF THE VERTEX ANGLES FOR EACH POLYGON

15-gon

50- gon

35-gon

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

1260°

1620°

### Angle Sum Measures of the Exterior Angles of a Polygon

LESSON 7

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
• 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

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°
• m4= 110
• m5= 100
• m6= 150
• m2 + m4 + m6=360

6

3

1

1

2

5

4

20°

160°

110°

70°

70°

110°

60°

120°

120°

60°

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

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

30°

10°

### QUIZ

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

24°

45°