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Angles

C

AB, BA, and AC

A

B

Course 1

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.

Angles

Course 1

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 Amy’s and Trisha’s angles is equal to the sum of the measures of Jack’s and Nate’s angles. The sum of the measures of all the angles is equal to 180°. What is the measure of each student’s angle?

Jack’s angle: 30°; Nate’s angle: 60°; Amy’s angle: 15°; Trisha’s angle: 75°

Angles

Course 1

Insert Lesson Title Here

Vocabulary

angle

vertex

acute angle

right angle

obtuse angle

straight angle

Angles

Course 1

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. The number of degrees determines the type of angle. Use the symbol °to show degrees: 90° means “90 degrees.”

Angles

Course 1

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

A straight angle measures exactly 180°.

Angles

F

H

G

Course 1

Additional Example 1: Measuring an Angle with a Protractor

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

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

Angles

F

H

G

Course 1

Additional Example 1 Continued

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

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

Angles

F

H

G

Course 1

Additional Example 1 Continued

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

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

Angles

F

H

G

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

Course 1

Additional Example 1 Continued

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

Angles

F

H

G

Course 1

Additional Example 1 Continued

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

- Since 120° > 90° and 120° < 180°, the angle is obtuse.

Angles

Course 1

Try This: Example 1

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

G

I

H

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

Angles

Course 1

Try This: Example 1 Continued

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

G

I

H

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

Angles

Course 1

Try This: Example 1 Continued

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

G

I

H

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

Angles

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

Course 1

Try This: Example 1 Continued

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

G

I

H

Angles

Course 1

Try This: Example 1 Continued

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

G

I

H

- Since 70° < 90°, the angle is acute.

Angles

Course 1

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.

Angles

Course 1

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.

Angles

Course 1

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 make at 80°.

Angles

Course 1

Try This: Example 2

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

- Draw a ray on a sheet of paper.

Angles

Course 1

Try This: Example 2 Continued

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

- 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.

Angles

Course 1

Try This: Example 2 Continued

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

- 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 make at 45°.

Angles

Course 1

To estimate the measure of an angle, compare it with an angle whose measure you already know. A right angle has half the measure of a straight angle. A 45° angle has half the measure of a right angle.

Angles

Course 1

Additional Example 3: Estimating Angle Measures

Estimate the measure of the angle, and then use a protractor to check the reasonableness of your estimate.

Think: The measure of the angle is about halfway between 90° and 180°. A good estimate would be 135°.

The angle measures 131°, so the estimate is reasonable.

Angles

Course 1

Try This: Example 3

Estimate the measure of the angle, and then use a protractor to check the reasonableness of your estimate.

Think: The measure of the angle is a little more than halfway between 0° and 90°. A good estimate would be 50°.

The angle measures 52°, so the estimate is reasonable.

Angles

Course 1

Insert Lesson Title Here

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°?

obtuse

acute

30°

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