8.1 – Find Angle Measures in Polygons

Interior Angle:

Exterior Angle:

Diagonal:

Angle inside a shape

Angle outsidea shape

Line connecting two nonconsecutive vertices

1 2

2

1

# of sides

Name of Polygon

# of triangles formed from 1

vertex

Sum of the measures of

interior angles

3 1 180°triangle

# of sides

Name of Polygon

# of triangles formed from

1 vertex

Sum of the measures of

interior angles

4 quadrilateral 2 360°

# of sides

Name of Polygon

# of triangles formed from

1 vertex

Sum of the measures of

interior angles

5 pentagon 3 540°

# of sides

Name of Polygon

# of triangles formed from

1 vertex

Sum of the measures of

interior angles

6 hexagon 4 720°

# of sides

Name of Polygon

# of triangles formed from

1 vertex

Sum of the measures of

interior angles

7

8

9

10

n

5 900°

6 1080°

7 1260°

8 1440°

n – 2 180(n – 2)

heptagon

octagon

nonagon

decagon

n-gon

The sum of the measures of the interior angles of a polygon are:_______________________180(n – 2)

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

180(n – 2) n

Find the sum of the measures of the interior angles of the indicated polygon.

18-gon

180(n – 2)

180(18 – 2)180(16)

2880°

Find the sum of the measures of the interior angles of the indicated polygon.

30-gon

180(n – 2)

180(30 – 2)180(28)

5040°

Find x.

180(n – 2)

180(5 – 2)180(3)

540°

x + 90 +143 + 77 + 103 = 540

x + 413 = 540

x = 127°

Find x.

180(n – 2)

180(4 – 2)180(2)

360°

x + 87 + 108 + 72 = 360

x + 267 = 360

x = 93°

Given the sum of the measures of the interior angles of a polygon, find the number of sides.

2340°

180(n – 2) = 2340

180n – 360 = 2340

180n = 2700

n = 15

Given the sum of the measures of the interior angles of a polygon, find the number of sides.

6840°

180(n – 2) = 6840

180n – 360 = 6840

180n = 7200

n = 40

Given the number of sides of a regular polygon, find the measure of each interior angle.

8 sides

180(n – 2) n

180(8 – 2) 8

180(6) 8

= =1080 8

=

135°=

Given the number of sides of a regular polygon, find the measure of each interior angle.

18 sides

180(n – 2) n

180(18 – 2) 18

180(16) 18

= =2880 18

=

160°=

Given the measure of each interior angle of a regular polygon, find the number of sides.

144°

180(n – 2) n

144=

1

144n = 180n – 360

0 = 36n – 360

360 = 36n10 = n

Given the measure of each interior angle of a regular polygon, find the number of sides.

108°

180(n – 2) n

108=

1

108n = 180n – 360

0 = 72n – 360

360 = 72n5 = n

Use the following picture to find the sum of the measures of the exterior angles.

ma =

mb =

mc =

md =

Sum of the exterior angles =

110°

60°

100°

90°360°

The sum of the exterior angles, one from each

vertex, of a polygon is: ____________________360°

The measure of each exterior angle of a

regular n-gon is: _________________________

360° n

Find x.

x + 137 + 152 = 360

x + 289 = 360

x = 71°

Find x.

x + 86 + 59 + 96 + 67 = 360

x + 308 = 360

x = 52°

Find the measure of each exterior angle of the regular polygon.

12 sides

360° n

= 360° 12

= 30°

Find the measure of each exterior angle of the regular polygon.

5 sides

360° n

= 360° 5

= 72°

Find the number of sides of the regular polygon given the measure of each exterior angle.

60°

360° n

= 60°1

60n = 360

n = 6

Find the number of sides of the regular polygon given the measure of each exterior angle.

24°

360° n

= 24°1

24n = 360

n = 15

Sum of Angles Each angle

Interior

Exterior

180(n – 2) n180(n – 2)

360° n360°

HW Problem8.1 510-512 3-15 odd, 16, 19, 24, 25, 29, 31

#1313. Find x.

180(n – 2)

180(8 – 2)

180(6)

1080°

x+143+2x+152+116+125+140+139=1080

3x + 815 = 1080

Ans:

x = 88.33°