Warm up the ol’ thinker Solve for x: HOMEWORK QUESTIONS? Pg 300 1-15.

Warm up the ol’ thinker

Solve for x:

1.) 155 115 2 360

2.)6 5 6 5 8 9 8 9 10 1 540

3603.) 15

( 2)1804.) 60

x x

x x x x x

x

x

x

HOMEWORK QUESTIONS?

• Pg 300 1-15

Ex. 1 Use the regular pentagon to answer the questions.

A)Find the sum of the measures of the interior angles.

B) Find the measure of ONE interior angle

540°

108°

Ex. 2 Use a regular 15-gon to answer the questions.

A) Find the sum of the measures of the interior angles.

B) Find the measure of ONE interior angle

2340°

156°

Find the measures of one interior angle of the indicated polygon.

1. Regular triangle

2. Regular heptagon

3. Regular dodecagon

What about the outside?Finding and using the exterior angle measures

of polygons

In any convex polygon, the sum of the

measures of the exterior angles, one at

each vertex, is 360°.

1

2

3

4

5

m m m m m 1 2 3 4 5 360

In any convex polygon, the sum of the measures of the

exterior angles, one at each vertex, is 360°.

1

3

2

m m m 1 2 3 360

In any convex polygon, the sum of the

measures of the exterior angles, one at

each vertex, is 360°.

1

3

2

4

m m m m 1 2 3 4 360

Ex. 1 Find the measure of ONE exterior angle of a regular hexagon.

60°

sum of the exterior anglesnumber of sides

3606

Ex. 2 Find the measure of ONE exterior angle of a regular heptagon.

51.4°

sum of the exterior anglesnumber of sides

3607

Ex. 3 Each exterior angle of a polygon is 18. How many sides does it have?

n = 20

angleexterior sides ofnumber

anglesexterior theof sum

18360

n

Find the measures of an interior angle and exterior angle of the indicated polygon.

1. Regular triangle

2. Regular 20-gon

3. Regular nonagon

4. Regular heptagon

5. Regular dodecagon

6. Regular 17-gon

How many sides does the polygon have?

1. Each interior angle has a measure of 140º

2. Each interior angle has a measure of 175.2º

3. Each exterior angle has a measure of 45º

4. Each exterior angle has a measure of 3º

Ex: 3 The measure of each interior angle is 150°, how many sides does the regular polygon have?

n

n 180)2(One interior angle

150180)2(

n

n

nn 150180)2(

nn 150360180 36030 n

12nA regular

dodecagon

142o

105o

140o

124o

xo88o

Find the value of x:

64o

3xo 2xo

110o86o

Find the value of x:

60o

100o

8xo

6xo

6xo

20o

Find the value of x:

The measures of the interior angles of a convex octagon are 45x, 40x, 155, 120,

155, 38x, 158, 41x. What is the measure of the smallest interior angle?

Homework:Pg 301 # 26 - 35