Warm Up 1. Two angles are supplementary. One angle measures 61°. Find the measure of the other...

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°

Course 2

8-4 Properties of Circles

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°

Course 2


Learn to identify parts of a circle and to find central angle measures.

Course 2


Vocabularycirclecenter of a circleradiusdiameterchordarccentral anglesector

Insert Lesson Title Here

Course 2


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.

Course 2


ArcPart of a circle named by its endpoints

RadiusLine segment whose endpoints are the centerof a circle and any point on the circle

Diameter

Line segment that passesthrough the center of a circle, and whose endpoints lie on the circle

ChordLine segment whose endpoints are any twopoints on a circle

Course 2


Name the parts of circle M.

Additional Example 1: Identifying Parts of a Circle

O

N

P

Q

R

M

A. radii:

B. diameters:

C. chords:

MN, MR, MQ, MO

NR, QO

NR, QO, QN, NP

Radii is the plural form of radius. Reading Math

Course 2


)

Central angle

Sector

A central angle of a circleis an angle formed by tworadii.

A sector of a circle is the part of the circleenclosed by two radii and anarc connecting them.

The sum of the measures of allof the central angles in a circleis 360°. We say that there are 360° in a circle.

Course 2


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.

Additional Example 2: Problem Solving Application

Course 2


11 Understand the Problem

The answer is the measure of the central angle that represents blueberry.

Additional Example 2 Continued

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.

Course 2


22 Make a Plan

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°

Solve33

0.40 · 360° = 144° Multiply.

The central angle of the sector is 144°.


Course 2


Look Back44

The 40% sector is less than half the graph, and 144° is less than half of 360°. Therefore, the answer is reasonable.


Course 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.

Check It Out: Example 2

Course 2


11 Understand the Problem

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.

Check It Out: Example 2 Continued

Course 2


22 Make a Plan

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°

Solve33

0.35 · 360° = 126° Multiply.

The central angle of the sector is 126°.


Course 2


Look Back44

The 35% sector is less than half the graph, and 126° is less than half of 360°. Therefore, the answer is reasonable.


Course 2


Lesson Quiz

Name the parts of circle B.

1. radii

2. diameter(s)

3. chord(s)

4.

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45°

A pie is cut into 8 equal sectors. Find the measure of the central angle of one slice ofpie.

BA, BC

AC

DE, FE, AC

Course 2


Warm Up 1. Two angles are supplementary. One angle measures 61°. Find the measure of the other...

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