The Polygon Angle-Sum Theorems Worksheet With Answers Page 6
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1
2
3
4
5
6
7
8Error Prevention!
Packaging
The nut container at the right has the
shape of a regular octagon. It fits in a square box.
Exercise 36
Ask: How many sides
A cheese wedge fills each corner of the box.
does this polygon have?
5
What is
26. Find the measure of each angle of a cheese wedge.
the sum of the interior angles for
45, 45, 90
this figure?
540°
27.
90
Critical Thinking
27.
Show how to rearrange
the four pieces of cheese to make a regular
Exercise 37
Have students
polygon. What is the measure of each angle
investigate the shapes of sports
of the polygon?
See left.
stadiums and report how polygons
are used in designing them.
B
B
Apply Your Skills
Use a protractor. Sketch each type of regular polygon.
90
Exercise 38
If necessary, review
120
60
Sample: dodecagon
90
how to solve equations with a
150
30
Use the protractor to equally space 12 points
variable in the denominator.
12 = 30 , so mark a point
around a circle. (360
Remind students that this is a
every 30 .) Connect these points to form a
180
0
regular polygon.
regular dodecagon.
28–31. See margin.
30
150
Technology Tip
28. triangle
29. quadrilateral
Exercise 57
This would be a nice
60
120
30. hexagon
31. octagon
90
classroom exercise using the table
feature of a graphing calculator
The sum of the measures of the angles of a polygon with n sides is given. Find n.
with overhead display.
32. 180
3
33. 1080
8
34. 1980
13
35. 2880
18
Connection to Algebra
B
D
36.
Multiple Choice
In the figure at right,
and
Exercise 58
Part b introduces
D
m C
130
B
. What is m
?
C
the idea of the asymptote of
25
50
a function, which students will
115
160
A
E
encounter in their next algebra
37.
Stage Design
The diagram at the right shows platforms
course.
1
constructed for a theater-in-the-round stage. Describe the
GPS
largest platform by the type of regular polygon it suggests.
Find the measure of each numbered angle.
2
octagon; m l 1
135; m l 2
45
Error Analysis
38.
Miles said that he measured an angle
of a regular polygon to be 130 . Explain why this result
2)180
(n
is impossible.
If you solve
130, you get n
7.2.
n
This number is not an integer.
39.
Critical Thinking
A triangle has two congruent angles and an exterior angle with
measure 100. Find two possible sets of measures for the angles of the triangle.
20-80-80; 50-50-80
Real-World
Connection
The measure of an exterior angle of a regular polygon is given. Find the measure of
an interior angle, and find the number of sides.
360
At a theater-in-the-round,
180
x;
x
seats are arranged so the
40. 72
108; 5
41. 36
144; 10
42. 18
162; 20
43. 30
150; 12
44. x
audience surrounds the stage.
28.
Probability
45.
Find the probability that the measure of an angle of a regular
4
n-gon is a positive integer if n is an integer and 3
n
12.
5
2
2
x
x
46.
Algebra
A polygon has n sides. An interior angle of the polygon and
an adjacent exterior angle form a straight angle.
a. What is the sum of the measures of the n straight angles?
n 180
29.
GO
(n – 2)180
b. What is the sum of the measures of the n interior angles?
Homework Help
c. Using your answers above, what is the sum of the measures
180n – 180(n – 2)
of the n exterior angles?
360
Visit:
Polygon Ext. l -Sum Thm.
d. What theorem do the steps above lead to?
Web Code: aue-0305
30.
162
Chapter 3
Parallel and Perpendicular Lines
57. a. (20, 162), (40, 171),
c. It is very close to 180.
58. b. As n gets larger, the
(60, 174), (80, 175.5),
size of the angles get
31.
d. No, two sides cannot
(100, 176.4), (120, 177),
closer to 180. The
be collinear.
(140, 177.4),
more sides it has, the
(160, 177.8),
closer the polygon is
(180, 178), (200, 178.2)
to a circle.
162
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