EXERCISES• TELL WHETHER OR NOT EACH

OF THE FOLLOWING IS A POLYGON.

Exercises • TELL WHETHER A POLYGON IS

CONVEX OR NOT.

POLYGONS POLYGONS and its partsand its partsPOLYGONS POLYGONS

and its partsand its partsReview Review

POLYGON PARTS

POLYGON PARTS

Side - one of the line segments that make

up the polygon.

Vertex - point where

two sides meet. Two or

more of these points

are called 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 non-overlapping diagonals

No. of Trianglesformed

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:

1. What is the sum of the measures of the interior angles of a convex polygon with

a. 11 sides b. 15 sides

Solutions:a. Sa = (n – 2) 180⁰

= (11 – 2) 180⁰

= 9(180⁰) = 1620⁰

Examples:

1. What is the sum of the measures of the interior angles of a convex polygon with

a. 11 sides b. 15 sides

Solutions:b. Sa = (n – 2) 180 ⁰

= (15 – 2) 180⁰ = 13(180⁰) = 2340⁰

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 1440 ?⁰

Solutions:b. Sa = (n – 2) 180⁰ 1440⁰ = (n – 2) 180⁰ 1440 = 180⁰ n – 360⁰

n =

n =

n = 10

180

3601440

180

1800The 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

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 Interior Angle - Angle

formed by two adjacent sides inside the polygon.

Exterior Angle - Angle

formed by two adjacent sides outside 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°

112

3

4

5

6

If m1= 70, what is the measure 4?

m4= 110 If m2 = 80, what is the

m5? m5= 100 If m3 = 30, what is the

m6? m6= 150

112

3

4

5

6

The sum of the exterior angles of an n-gon is 360°

m4= 110m5= 100m6= 150

m2 + m4 + m6=360 112

3

4

5

6

160°

70°

120°120°

70°

60°

110°

20°

60°

110°

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

Quadrilateral

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:Ea =

Ea =

= 60

 

n

360

6

360

FIND THE NUMBER OF SIDES OF A REGULAR POLYGON WHEN THE

MEASURE OF THE EXTERIOR ANGL E IS GIVEN

1.30°

2.10°

QUIZQUIZQUIZQUIZ

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°