POLYGONS

Triangle eight sides

Heptagon three sides

Octagon seven sides Pentagon four sides

Hexagon five sides

Square six sides

Check your Knowledge: Matching

Triangle six sides

Heptagon three sides

Octagon five sides Pentagon four sides

Hexagon seven sides

Square eight sides

Concave Congruent Convex Corresponding Regular Right

Check your Knowledge: Fill in the Blank

1. A ______________ polygon exists if no line that contains a side of the polygon contains a point in the interior of the polygon.

2. A ______________ polygon is a polygon that is not convex.

3. A ______________ polygon is both equilateral and equiangular.

Concave Congruent Convex Corresponding Regular Right

Check your Knowledge: Fill in the Blank

1. A ______________ polygon exists if no line that contains a side of the polygon contains a point in the interior of the polygon.

2. A ______________ polygon is a polygon that is not convex.

3. A ______________ polygon is both equilateral and equiangular.

Convex

Concave

Regular

vertex

side

vertexB

A

E

D

C

Parts of a Polygon

R

Q

P

S

T

Name the Polygon

Name the Polygon

R

Q

P

S

T

PQRST

Examples: Name the Polygons

D

E

F

K L

J M

A

B

F

D C

E

V

Y

Z

W

X

Sum of the interior angle measures

3 methods for you to choose from

Polygon

n number of sides

number of triangles formed

Sum of the interior angle measures

triangle 3

quadrilateral 4

pentagon 5

hexagon 6

septagon 7

octagon 8

Method 1:

Polygon

n number of sides

number of triangles formed

Sum of the interior angle measures

triangle 3 1

quadrilateral 4 2

pentagon 5 3

hexagon 6 4

septagon 7 5

octagon 8 6

Polygon

n number of sides

number of triangles formed

Sum of the interior angle measures

triangle 3 1 180

quadrilateral 4 2 2 X 180 = 360

pentagon 5 3 3 X 180 = 540

hexagon 6 4 4 X 180 =720

septagon 7 5 5 X 180 =900

octagon 8 6 6x 180 =1080

• The sum of the measures of the angles of an n-gon is

(n-2)180

Method 2:

Method 3:

• You know that the sum of the interior angles of every triangle is 180 –

• For each side you add to a triangle to make the shape you need, you add 180.

Find the measure of an interior angle and an exterior angle for the indicated

regular polygon

• Regular 18-gon

Find the measure of an interior angle and an exterior angle for the indicated

regular polygon

• Regular 18-gon • Interior Angles• (n-2)*180 = 2880• 2880/18 = 160

The value of x is 72.

103°, 103°

82

112

132107

x

The measures of three of the interior angles of a quadrilateral are 89°, 110°, and 46°. Find the measure of the fourth interior angle.

82

112

132107

x

The measures of three of the interior angles of a quadrilateral are 89°, 110°, and 46°. Find the measure of the fourth interior angle.

115°

107°

Polygon Exterior Angle-Sum Theorem

The sum of the measures of the exterior angles of a polygon,

one at each vertex, is 360.