Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
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Warm Up 1. Two angles are supplementary. One
angle measures 61. Find the measure of the other
angle. 2. Two angles are complementary. One
angle measures 19. Find the measure of the other
angle. 3. Two angles are supplementary and
congruent. Find the measure of each angle.
119
71
90
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Problem of the Day In a circle graph, three
sectors representing 15, 25, and 30 are
labeled. What percent does the fourth sector
represent, and what is its measure in degrees?
30 108
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Learn to identify parts of a circle and to find
central angle measures.
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Insert Lesson Title Here
Vocabulary
circle center of a circle radius diameter chord ar
c central angle sector
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A circle is the set of all points in a plane that
are the same distance from a given point, called
the center of a circle.
A circle is named by its center. For example, if
point A is the center of a circle, then the name
of the circle is circle A. There are special
names for the different parts of a circle.
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Diameter
Arc Part of a circle named by its endpoints
Line segment that passes through the center of a
circle, and whose endpoints lie on the circle
Radius
Line segment whose endpoints are the center of a
circle and any point on the circle
Chord
Line segment whose endpoints are any two points
on a circle
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Additional Example 1 Identifying Parts of a
Circle
Name the parts of circle M.
N
A. radii
O
P
B. diameters
M
Q
C. chords
R
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Check It Out Example 1
Name the parts of circle M.
B
A
C
A. radii
G
B. diameters
D
H
F
C. chords
E
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Sector
A central angle of a circle is an angle formed by
two radii. A sector of a circle is the part of
the circle enclosed by two radii and an arc
connecting them.
)
The sum of the measures of all of the central
angles in a circle is 360. We say that there are
360 in a circle.
Central angle
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Additional Example 2 Problem Solving Application
The circle graph shows the results of a survey
about favorite types of muffins. Find the central
angle measure of the sector that shows the
percent of people whose favorite type of muffin
is blueberry.
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Additional Example 2 Continued
The answer is the measure of the central angle
that represents blueberry.
List the important information The percent of
people whose favorite muffin is blueberry is
40. The central angle measure of the sector
that represents this group is 40 of the 360 of
the circle.
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Additional Example 2 Continued
There are 360 in a circle. Since the sector is
40 of the circle graph, the central angle is 40
of the 360 in the circle.
40 of 360 0.40 360
0.40 360 144
Multiply.
The central angle of the sector is 144.
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Additional Example 2 Continued
Look Back
The 40 sector is less than half the graph, and
144 is less than half of 360. Therefore, the
answer is reasonable.
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Check It Out Example 2
The circle graph shows the results of a survey
about the favorite types of muffins. Find the
central angle measure of the sector that shows
the percent of people whose favorite type of
muffin is banana nut.
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Check It Out Example 2 Continued
The answer is the measure of the central angle
that represents banana nut.
List the important information The percent of
people whose favorite muffin is banana nut is
35. The central angle measure of the sector
that represents this group is 35 of the 360 of
the circle.
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Check It Out Example 2 Continued
There are 360 in a circle. Since the sector is
35 of the circle graph, the central angle is 35
of the 360 in the circle.
35 of 360 0.35 360
0.35 360 126
Multiply.
The central angle of the sector is 126.
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Check It Out Example 2 Continued
Look Back
The 35 sector is less than half the graph, and
126 is less than half of 360. Therefore, the
answer is reasonable.
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Insert Lesson Title Here
Lesson Quiz
Name the parts of circle B. 1. radii 2.
diameter(s) 3. chord(s) 4.
A pie is cut into 8 equal sectors. Find the
measure of the central angle of one slice of pie.
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