Holt CA Course 1

9-2 Measuring and Classifying Angles

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California StandardsCalifornia Standards

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Holt CA Course 1

9-2 Measuring and Classifying AnglesWarm Up

1. Draw two points. Label one point A and

the other point B.

2. Draw a line through points A and B.

3. Draw a ray with A as an endpoint and C

as a point on the ray.

4. Name all the rays in your drawing.

AB, BA, and AC

A B

C

Holt CA Course 1

9-2 Measuring and Classifying Angles

Preparation for MG2.1 Identify angles as vertical, adjacent, complementary, or supplementary and provide descriptions of these terms.Also covered: Prep for MG2.3

California Standards

Holt CA Course 1

9-2 Measuring and Classifying Angles

Vocabulary

anglevertexacute angleright angleobtuse anglestraight angle

Holt CA Course 1

9-2 Measuring and Classifying Angles

An angle is formed by two rays with a common endpoint, called the vertex. An angle can be named by its vertex or by its vertex and a point from each ray. The middle point in the name should always be the vertex.

Angles are measured in degrees. Use the symbol ° to show degrees.

Holt CA Course 1

9-2 Measuring and Classifying AnglesAdditional Example 1: Measuring an Angle with a

Protractor

Use a protractor to measure the angle.

• Place the center point of the protractor on the vertex of the angle.

G H

F

Holt CA Course 1

9-2 Measuring and Classifying AnglesAdditional Example 1 Continued

Use a protractor to measure the angle.

• Place the protractor so that ray GH passes through the 0° mark.

G H

F

Holt CA Course 1

9-2 Measuring and Classifying Angles

• Using the scale that starts with 0° along ray GH, read the measure where ray GF crosses.

Additional Example 1 Continued

Use a protractor to measure the angle.

G H

F

Holt CA Course 1

9-2 Measuring and Classifying Angles

mFGH is read “the measure of angle FGH.”

Reading Math

Holt CA Course 1

9-2 Measuring and Classifying Angles

• The measure of FGH is 120°. Write this as mFGH = 120°.

Additional Example 1 Continued

Use a protractor to measure the angle.

G H

F

Holt CA Course 1

9-2 Measuring and Classifying AnglesCheck It Out! Example 1

Use a protractor to measure the angle.

H I

G

• Place the center point of the protractor on the vertex of the angle.

Holt CA Course 1

9-2 Measuring and Classifying AnglesCheck It Out! Example 1 Continued

Use a protractor to measure the angle.

• Place the protractor so that ray HI passes through the 0° mark.

H I

G

Holt CA Course 1

9-2 Measuring and Classifying AnglesCheck It Out! Example 1 Continued

Use a protractor to measure the angle.

H I

G

• Using the scale that starts with 0° along ray HI, read the measure where ray HG crosses.

Holt CA Course 1

9-2 Measuring and Classifying AnglesCheck It Out! Example 1 Continued

Use a protractor to measure the angle.

H I

G

• The measure of GHI is 70°. Write this as mGHI = 70°.

Holt CA Course 1

9-2 Measuring and Classifying Angles

Additional Example 2: Drawing an Angle with a Protractor

Use a protractor to draw an angle that measures 80°.

• Draw a ray on a sheet of paper.

Holt CA Course 1

9-2 Measuring and Classifying AnglesAdditional Example 2 Continued

Use a protractor to draw an angle that measures 80°.

• Place the center point of the protractor on the endpoint of the ray.

• Place the protractor so that the ray passes through the 0° mark.

Holt CA Course 1

9-2 Measuring and Classifying AnglesAdditional Example 2 Continued

Use a protractor to draw an angle that measures 80°.

• Make a mark at 80° above the scale on the protractor.

• Use a straightedge to draw a ray from the endpoint of the first ray through the mark you made at 80°.

Holt CA Course 1

9-2 Measuring and Classifying Angles

Check It Out! Example 2

Use a protractor to draw an angle that measures 45°.

• Draw a ray on a sheet of paper.

Holt CA Course 1

9-2 Measuring and Classifying Angles

• Place the center point of the protractor on the endpoint of the ray.

• Place the protractor so that the ray passes through the 0° mark.

Check It Out! Example 2 Continued

Use a protractor to draw an angle that measures 45°.

Holt CA Course 1

9-2 Measuring and Classifying Angles

• Make a mark at 45° above the scale on the protractor.

• Use a straightedge to draw a ray from the endpoint of the first ray through the mark you made at 45°.

Check It Out! Example 2 Continued

Use a protractor to draw an angle that measures 45°.

Holt CA Course 1

9-2 Measuring and Classifying Angles

An acute angle measures less than 90°.

A right angle measures exactly 90°.

Right angles are usually marked with a symbol.

Reading Math

Holt CA Course 1

9-2 Measuring and Classifying Angles

An obtuse angle measures more than 90° and less than 180°.

A straight angle measures exactly 180°.

Holt CA Course 1

9-2 Measuring and Classifying Angles

Additional Example 3: Classifying Angles

Classify each angle as acute, right, obtuse, or straight.

A. B.

The angle measures less than 90°, so it is an acute angle.

The angle measures exactly 90°, so it is a right angle.

Holt CA Course 1

9-2 Measuring and Classifying Angles

Check It Out! Example 3

Classify each angle as acute, right, obtuse, or straight.

A. B.

The angle measures less than 90°, so it is an acute angle.

The angle measures exactly 180°, so it is a straight angle.

Holt CA Course 1

9-2 Measuring and Classifying AnglesAdditional Example 4: Application

A welder used this piece of metal on his project. Classify X, Y, and Z.

X right

Y obtuse

Z acute

The angle is marked as a right angle.

The angle measures more than 90° and less than 180°.

The angle measures less than 90°.

Holt CA Course 1

9-2 Measuring and Classifying AnglesCheck It Out! Example 4

A metal jeweler used this piece of metal on her project. Classify A, B, and D.

D

C

A

B

A obtuse

B acute

D right The angle is marked as a right angle.

The angle measures more than 90° and less than 180°.

The angle measures less than 90°.

Holt CA Course 1

9-2 Measuring and Classifying AnglesLesson Quiz

Use a protractor to draw an angle with the given measure. Tell what type of angle it is.

1. 140°

2. 20°

3. Draw a right angle.

4. Is the angle shown closer to 30° or 120°?

Check student drawings: acute

Check student drawings; obtuse

30°