Warm Up

C

BA

C

D

ba

70

<ACB is a right angle, find the values of a, b, and c.

Polygon Number of Sides Number of Triangles Formed

Sum of the Interior Angle Measures

4

5

6

7

8

1. Sketch Polygons with each number of sides. 2. Divide each polygon into triangles by drawing all diagonals that are

possible from one vertex.3. Find the sum of the measures of each polygon using triangle angle sum

theorem.4. Look for patterns in the table, write a rule for the sum of the measures of

the angles of an n-gon.

The Sum of Polygon Angle Measures

Polygon Angle Sum Theorem

The sum of the interior angle measure of a convex polygon with n sides is

(n – 2)180°

Whiteboards

Send one person from each table to get a whiteboard for every person at their table and two rags(erasers).

Examples

Use your conjectures to calculate the measure of each lettered angle.

1. 2.

47

73

120

62116

85x

x

More Examples……

3.4. 78

83 a

93

77

97a

b c

de

77

Find e

And some more for the road..

5. Find the sum of the measures of the angles of 16-gon.

And another…

6. The sum of the measures of the interior angles of a regular polygon is 2340. How many sides does the polygon have?

For any polygon, the sum of the measures of a set of exterior angles is 360°.

For the hexagon: m<1 + m<2 + m<3 + m<4 + m<5 + m<6 = 360°

Exterior Angle Sum Theorem

3

24

5

16

Examples

1. How many sides does a polygon have if each exterior angle measures 30°?

2. What is the measure of an exterior angle of an equiangular hexagon?

And again

Find x.3. 4.

116°

80°

a

x

x

2x

3x

a

b

c

82°

72°

134°

Linear Review!

Homework

• Page 161-163 #1-25 odd, 47-49 DUE MONDAY!

• Linear worksheet• DUE Tuesday (Period 1)• Due Wednesday (Period 2,

4)

Try these

• 2h

• 2h• h

• h

y

110

87x

100

x

y

m

97

99

s

60

y87

r

p

1.2.

3.

4.