6-1: Polygon Angle-Sum Theorems - North Hunterdon-Voorhees ...

CP Geometry

Shapes for the next page. Draw all the diagonals possible from only one vertex. Use the information in the chart on the next page.

Find the measures of the interior angles of the following polygons. Complete the table below. Use the shapes on the previous page.

Polygon

# of Sides

# of s Formed

Sum of Interior Angle Measures

Quadrilateral

4

Pentagon

5

Hexagon

6

Heptagon

7

Octagon

8

2

2*180=360

3

3*180=540

4

4*180=720

5

5*180=900

6

6*180=1080

Polygon Angle-Sum Theorem

The sum of the measures of the interior angles of an n-gon

is:

n 2180

Examples: Find the sum of the measures of the following polygons:

a). Decagon 10 2180 8*180 1440

b). 15-gon

15 2180 13*180 2340

c). dodecagon 12 2180 10*180 1800

Complete Got It? #1 p. 353 a. 2700

b. 1980 ? 180 + 2 = 13 sides

Find the value of x in each polygon.

V

W

122? x? 120 118 117 121122 mW 720

U 121?

120? R

598 mW 720 mW 122

117? 118?

Q

T

S

82?

86 118 129 82 mR 540 P 129?

x? R

415 mR 540 118?

mR 125 T

86?

S

Types of Polygons

Equilateral Polygon Equiangular Polygon Regular Polygon

Corollary to the Polygon Angle-Sum Theorem

The measure of each interior angle of a regular n-gon is:

n 2180

Complete Got It? #2 p. 354

n

9 - 2 180 7 180

9

= 9 = 140?

1

Exterior Angles of a Polygon

Find the sum of the exterior angles, one from each

vertex of the following polygons.

90?

90? 86? 94?

115?

65?

110? 70?

16? 164?

75?

100?

86 110 164 360

80?

90 115 80 75 360

Polygon Exterior Angle Sum Theorem

The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360?.

m1 m2 m3 m4 m5 360

2 1

5

Complete Got It? #4 p. 355

360 9 = 40?

3 4

Homework: p. 356 #18-25, 29-36, 41

2

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