1. 1. Draw two points. Label one point A and the other point B.
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. C
AB, BA, and AC A B

2. 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°

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

4. Vocabulary angle vertex acute angle right angle obtuse angle
straight angle

5. 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.

6. Additional Example 1: Measuring an Angle with a Protractor
Use a protractor to measure the angle. Tell what angle it is. G H F
Place the center point of the protractor on the vertex of the angle.

7. Additional Example 1 Continued
Use a protractor to measure the angle. G H F
Place the protractor so that ray GH passes through the 0° mark.

8. Additional Example 1 Continued
Use a protractor to measure the angle. G H F
Using the scale that starts with 0° along ray GH, read the measure where ray GF crosses.

9. Reading Math
mFGH is read “the measure of angle FGH.”

10. Additional Example 1 Continued
Use a protractor to measure the angle. G H F
The measure of FGH is 120°. Write this as m FGH = 120°.

11. Check It Out: Example 1
Use a protractor to measure the angle. G I H
Place the center point of the protractor on the vertex of the angle.

12. Check It Out: Example 1 Continued
Use a protractor to measure the angle. G I H
Place the protractor so that ray HI passes through the 0° mark.

13. Check It Out: Example 1 Continued
Use a protractor to measure the angle. G I H
Using the scale that starts with 0° along ray HI, read the measure where ray HG crosses.

14. Check It Out: Example 1 Continued
Use a protractor to measure the angle. G I H
The measure of GHI is 70°. Write this as m GHI = 70°.

15. 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.

16. 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.

17. 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°.

18. Use a protractor to draw an angle that measures 45°.
Check It Out: Example 2
Use a protractor to draw an angle that measures 45°.
Draw a ray on a sheet of paper.

19. Use a protractor to draw an angle that measures 45°.
Check It Out: 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.

20. Use a protractor to draw an angle that measures 45°.
Check It Out: 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 made at 45°.

21. 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

22. An obtuse angle measures greater than 90° and less than 180°.
A straight angle measures exactly 180°.

23. 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.

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

25. 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
The angle is marked as a right angle.
Y obtuse
The angle measures greater than 90° and less than 180°.
Z acute
The angle measures less than 90°.

26. The angle measures greater than 90° and less than 180°.
Check It Out: Example 4
A metal jeweler used this piece of metal on her project. Classify A, B, and D. A D B C
A obtuse
The angle measures greater than 90° and less than 180°.
B acute
The angle measures less than 90°.
D right
The angle is marked as a right angle.

27. 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; obtuse
Check student drawings; acute
30°