Warm up the ol’ thinker Solve for x: 1.) 155 115 2 360 2.)6 5 6 5 8 9 8 9 10 1 540 360 3.) 15 ( 2)180 4.) 60 x x x x x x x x x x
Dec 15, 2015
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