7-2 Angles

Course 2

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Warm UpDraw each figure.

1. line segment

2. line

3. ray

4. plane

Course 2

7-2 Angles

Problem of the Day

What is the measure of the smaller angle between the hour hand and the minute hand on a clock at eight o’clock?120°

Course 2

7-2 Angles

Learn to identify angles and parts of angles.

Course 2

7-2 Angles

Vocabularyanglevertexright angleacute angleobtuse anglestraight anglecomplementary anglessupplementary angles

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Course 2

7-2 Angles

Course 2

7-2 Angles

An angle is formed by two rayswith a common endpoint. The two rays are the sides of the angle. The common endpoint isis the vertex.

You can name an angle in three ways:

• with the capital letter at the vertex: B,

• with the number inside the angle: 1,

• with three capital letters so that the letter at the vertex is in the middle: ABC or CBA

A

CB

1

Vertex

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7-2 Angles

Angles are measured in degrees (°). You can use a protractor to measure an angle.

The measure of XYZ is 122°, or m XYZ = 122°.

Give the measurement of each angle.

Additional Example 1A & 1B: Identifying Angle Measures

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7-2 Angles

A. STV

B. XTU

m STV = 55°

m XTU = 25°

Give the measurement of each angle.

Additional Example 1C &1D: Identifying Angle Measures

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7-2 Angles

C. WTU

D. STX

m WTU = 40° + 25°

m STX = 155°

m WTU = 65°

m STX = 55° + 60° + 40°

Try This: Example 1

Give the measure of each angle.

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7-2 Angles

A. STV

B. XTU

m STV = 35°

m XTU = 40°

35°

55° 50°

40°S

VW

X

U

T

Try This: Example 1 Continued

Give the measure of each angle.

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Course 2

7-2 Angles

C. WTU

D. STX

m WTU = 50° + 40°

m STX = 140°

m WTU = 90°

m STX = 35° + 55° + 50°

35°

55° 50°

40°S

VW

X

U

T

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7-2 Angles

An angle’s measure determines the type of angle it is.

A right angle is an angle that that measures exactly 90°. Thesymbol indicates a right angleAn acute angle is an anglethat measures less than 90°

An obtuse angle is an anglethat measures more than 90°but less than180°

A straight angle is an anglethat measures 180°

Tell whether each angle is acute, right, obtuse or straight.

Additional Example 2: Classifying Angles

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7-2 Angles

A. B. C.

right angle obtuse angle acute angle

Try This: Example 2

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7-2 Angles

Tell whether each angle is acute, right, obtuse, or straight.

A. B. C.

straight angle acute angle obtuse angle

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7-2 Angles

If the sum of the measures of two angles is90°, then the angles are complementary angles. If the sum of the measures of twoangles is 180°, then the angles are supplementary angles.

Use the figure to name the following.

Additional Example 3A: Identifying Complementary and Supplementary Angles

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7-2 Angles

A. one pair of complementary angles

Since 30° + 60° = 90°,

m OMP = 30° and m OMR = 60°

OMP and OMR are complementary.

60° 90°

30°60°

N Q

P

OR

M

Use the figure to name the following.

Additional Example 3B: Identifying Complementary and Supplementary Angles

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7-2 Angles

B. one pair of supplementary angles m RMO = 60° and m QMO = 90° + 30° = 120°

Since 60° + 120° = 180°, RMO and QMO are supplementary.

60° 90°

30°60°

N Q

P

OR

M

Use the figure to name the following.

Try This: Example 3A

Course 2

7-2 Angles

A. one pair of complementary angles

Since 30° + 60° = 90°,

m OMP = 30° and m NMQ = 60°

OMP and NMQ are complementary.

60° 90°

30°60°

N Q

P

OR

M

Use the figure to name the following.

Try This: Example 3B

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7-2 Angles

B. one pair of supplementary angles m QMP = 90° and m PMR = 30° + 60° = 90°

Since 90° + 90° = 180°, QMP and PMR are supplementary.

60° 90°

30°60°

N Q

P

OR

M

Lesson QuizGive the measure of each angle, and tell whether it is acute, obtuse, right, or straight.

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7-2 Angles

1. AFB

2. AFC

3. DFC

4. Name a pair of complementary angles.

5. Name a pair of supplementary angles.

90°; right

140°; obtuse

DFC and CFB

Possible answer: EFA and AFB

40°; acute50°

40°

A

B

CD

E F