8-2 Measuring and Classifying Angles

Warm 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

8-2 Measuring and Classifying Angles

Problem of the Day

The measure of Jack’s angle is twice that of Amy’s and half that of Nate’s. The sum of the measures of all the angles is equal to 105°. What is the measure of each student’s angle?

Jack’s angle: 30°; Nate’s angle: 60°; Amy’s angle: 15°

8-2 Measuring and Classifying Angles

Learn to name, measure, draw, and classify angles.

8-2 Measuring and Classifying Angles

Vocabulary

anglevertexacute angleright angleobtuse anglestraight angle

8-2 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 must be the vertex.

Angles are measured in degrees. The number of degrees determines the type of angle. Use the symbol ° to show degrees.

8-2 Measuring and Classifying Angles

Additional Example 1: Measuring an Angle with a Protractor

Use a protractor to measure the angle. Tell what angle it is.

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

G H

F

8-2 Measuring and Classifying Angles

Additional 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

8-2 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

8-2 Measuring and Classifying Angles

mFGH is read “the measure of angle FGH.”

Reading Math

8-2 Measuring and Classifying Angles

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

Additional Example 1 Continued

Use a protractor to measure the angle.

G H

F

8-2 Measuring and Classifying Angles

Check 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.

8-2 Measuring and Classifying Angles

Check 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

8-2 Measuring and Classifying Angles

Check 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.

8-2 Measuring and Classifying Angles

Check It Out: Example 1 Continued

Use a protractor to measure the angle.

H I

G

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

8-2 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.

8-2 Measuring and Classifying Angles

Additional 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.

8-2 Measuring and Classifying Angles

Additional 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°.

8-2 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.

8-2 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°.

8-2 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°.

8-2 Measuring and Classifying Angles

An acute angle measures greater than 0° and less than 90°.

A right angle measures exactly 90°.

Right angles are usually marked with a symbol.

Reading Math

8-2 Measuring and Classifying Angles

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

A straight angle measures exactly 180°.

8-2 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.

8-2 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.

8-2 Measuring and Classifying Angles

Additional Example 4: Application

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

X

W

Y

Z

X right

Y obtuse

Z acute

The angle is marked as a right angle.

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

The angle measures less than 90°.

8-2 Measuring and Classifying Angles

Check 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 greater than 90° and less than 180°.

The angle measures less than 90°.

8-2 Measuring and Classifying Angles

Lesson 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°