# 9.4: Angle Measurement

**At Grade**Created by: CK-12

Angles are tricky things. Have you ever tried to measure or draw an angle?

Cassie is working with a protractor in math class. She has been assigned the task of drawing a 35 degree angle. She is wondering if this angle will work for a ramp at the skateboard park. The trouble is that she isn't sure how to draw one or what one will look like.

Do you know?

**This Concept will teach you how to draw angles using a protractor. When finished, you will know what a 35 degree angle will look like.**

### Guidance

We just finished naming angles using points on the rays and the vertex. **We can also measure angles**. If you look at the two angles that you just named, you will see that they are different sizes. Angles are measured in ** degrees**. The larger the angle the higher the number of degrees.

**How can we measure angles?**

Angles are measured using a special tool called a ** protractor**.

Here is a picture of a protractor.

**Notice that you can see all of the degrees on the protractor.**

**How can we use a protractor?**

- First, you line up the vertex with the little hole in the middle of the protractor, then carefully align the bottom ray with the bottom line of the protractor.
- Then, you follow the top ray to the number of degrees that the angle measures.

Here's a few for you to try. Answer the following questions about angles.

#### Example A

How many degrees are in a straight line?

**Solution: 180 degrees**

#### Example B

If one ray of the angle is to the left of 90, is the angle less than 90 or greater than 90?

**Solution: The angle is less than 90.**

#### Example C

If an angle measures 120 degrees, is one of the rays to the left or right of 90?

**Solution: To the right of 90**

Remember Cassie and the angle? Here is the original problem once again.

Cassie is working with a protractor in math class. She has been assigned the task of drawing a 35 degree angle. She is wondering if this angle will work for a ramp at the skateboard park. The trouble is that she isn't sure how to draw one or what one will look like.

To draw an angle, first you have to draw a line segment that will serve as the bottom ray of the angle. Then you can measure 35 degrees and here is what the angle will look like.

**This angle is 35 degrees.**

### Vocabulary

Here are the vocabulary words in this Concept.

- Point
- a location in space that does not have size or shape.

- Ray
- a line that has one endpoint and continues indefinitely in one direction.

- Line
- a set of connected points without endpoints.

- Line Segment
- a set of connected points with two endpoints.

- Point of Intersection
- the point where two intersecting lines meet.

- Intersecting Lines
- lines that cross or meet at some point

- Parallel Lines
- Lines that do not cross or meet EVER and are equidistant.

- Angle
- a geometric figure formed by two rays that connect at a single point or vertex.

- Vertex
- The point of intersection of the lines or rays that form an angle

- Protractor
- a tool used to measure an angle in terms of degrees.

### Guided Practice

Here is one for you to try on your own.

Look at the following angles. Use a protractor to measure each angle.

**Answer**

First, line up your protractor to measure each angle. Be sure that the vertex is at 0. Then write down each number of degrees.

1. 120 degrees

2. 180 degrees

3. 35 degrees

4. 90 degrees

### Video Review

Here is a video for review.

Khan Academy: Using a Protractor

### Practice

Directions: Draw the following angles. Be sure to use a protractor and check your work with a friend.

1. 180 degrees

2. 100 degrees

3. 90 degrees

4. 15 degrees

5. 20 degrees

6. 45 degrees

7. 60 degrees

8. 110 degrees

9. 25 degrees

10. 160 degrees

11. 180 degrees

12. 140 degrees

13. 42 degrees

14. 115 degrees

15. 173 degrees

### Image Attributions

Here you'll learn to draw angles using a protractor.