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### POLYGONS and its parts

### Angle Sum Measures of the Exterior Angles of a Polygon WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN

### QUIZ MEASURE OF THE EXTERIOR ANGL E IS GIVEN

EXERCISES

- TELL WHETHER OR NOT EACH OF THE FOLLOWING IS A POLYGON.

Exercises

- TELL WHETHER A POLYGON IS CONVEX OR NOT.

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 =(S180) + 2

= (1260 180) + 2

= 7 + 2

n= 9

QUIZ THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN

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

1260°

1620°

LESSON 7

POLYGON PARTS WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN

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

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

Investigate WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN

- 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 m1= 70, what is the measure 4? WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN
- m4= 110
- If m2 = 80, what is the m5?
- m5= 100
- If m3 = 30, what is the m6?
- m6= 150

6

3

1

1

2

5

4

The sum of the exterior angles of an n-gon is 360° WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN

- m4= 110
- m5= 100
- m6= 150
- m2 + m4 + m6=360

6

3

1

1

2

5

4

20° WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN

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 WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN

Examples: WHEN THE SUM OF THE MEASURES OF THE VERTEX ANGLES IS GIVEN

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°

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°

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