6.1 Properties and Attributes of Polygons. Polygon Vocab POLYGON: Diagonal: Concave Polygons: Convex...

6.1

Properties and Attributes of Polygons

Polygon Vocab POLYGON:

Diagonal:

Concave Polygons:

Convex polygons:

Regular polygon:

Name the polygon by how many sides it has.

Sum of interior angles (& each angle!)

Sum interior angles = (n – 2)•180º Ex 1: Find the sum of the measures of interior angles of

the convex polygon: (*Think – how many triangles will it divide into?)

a) hexagon

b) decagon

c) 13-gon

b) 121-gon

Ex 2: Find the value of x

3x-2

3x

3x+4

4x-5

4x

x+3

1) Find sum of all interior angles

2) Set up equation

Ex 3: The sum of the interior angles = 2700º. Find the # of sides.

Ex 4: Find the number of sides (n) of the convex regular polygon if…

(Formula to find the sum of angles: ___________________)

ONE interior angle = 160º

Exterior Angles of a polygon:Find each exterior angle 1 =

2 = 3 = 4 = 5 =

Sum = 54

3

2

1

80 150

120

80

110

Ex 6: Find the value of x

6x

4x - 10

8x + 6

5x + 4

x

For ALL Convex Polygons Sum of exterior angles

Sum = 360º

ONE exterior angle of a regular n-gon is:Exterior = 360

n

In Summary… Sum interior angles of a convex n-gon is:

Sum = (n – 2)180

One interior angle of a regular n-gon is: ( 2)180n

n

Ex 7: Find the measure of each exterior and interior angle if given the # of sides of a regular polygon. 7 sides

Exterior Angle Interior Angle

19 sides Exterior Angle Interior Angle